delivered the opinion of the court:
Following a jury trial in the circuit court of Cook County, defendant, William Peeples, was convicted of first degree murder, home invasion, and aggravated arson. (Ill. Rev. Stat. 1987, ch. 38, pars. 9 — 1(a)(1), 12— ll(aX2), 20 — 1.1.) The trial judge sentenced defendant to *440death on the murder conviction and concurrent 30-year prison terms on the home invasion and aggravated arson convictions. The death sentence has been stayed (134 Ill. 2d R. 609(a)), and the case is now before us for direct review (Ill. Const. 1970, art. VI, §4(b); Ill. Rev. Stat. 1987, ch. 38, par. 9-l(i); 134 Ill. 2d R. 603).
We affirm defendant’s convictions and sentence.
The record contains the following pertinent facts. The State’s evidence at trial was essentially as follows. On May 18, 1988, the victim, Dawn Dudovic, and Pamela Killeen were roommates at an apartment complex in Schaumburg, Illinois. Defendant and his fiancee, Vanessa Allen, lived in an apartment adjacent to the victim’s apartment.
On the morning of May 18, Killeen heard the victim leave the apartment and lock the door. Killeen left the apartment later that morning to go to work.
At approximately 5:40 p.m., Killeen returned home. She saw the victim’s automobile in the parking lot. At the apartment door, Killeen began to retrieve her keys because she and the victim automatically locked their apartment door whenever each arrived home. However, Killeen noticed that a piece of paper towel stained with blood was wedged in the door, which prevented the door from locking.
Killeen removed the piece of paper towel. Entering the apartment, she dropped the paper towel by the door. Killeen saw their vacuum cleaner in the middle of the hallway and a mound of what was subsequently identified as sugar on the carpet. She saw blood also on the vacuum and the carpet.
When Killeen looked into the kitchen, she saw the victim lying on her back on the kitchen floor. The back of the victim’s dress was pulled up to the buttocks, while *441the front of the dress was pulled up to the waist, exposing her pantyhose and underwear.
Killeen immediately sought help. She pounded on the door of defendant’s apartment and screamed for help. Killeen did this for about one minute because she heard the sound of a radio or television inside the apartment. However, no one answered.
Killeen then sought and received the aid of another neighbor, Kenneth Evensen. Evensen looked into the kitchen, but did not enter. He saw the victim lying on her back, “stretched out in a pool of blood.” He observed also that the victim’s dress was “kind of hiked up over [sic] up to her waist.” Evensen and Killeen returned to his apartment and telephoned paramedics.
Schaumburg fire department paramedic Anthony Licata and his partner, Keith Kopecky, were dispatched to the apartment complex.
Licata proceeded to the kitchen, where he saw the victim lying in a large pool of blood. The victim’s dress was bloodstained and parts of it were soaked in blood. Licata remembered that the victim’s dress was “kind of raised up a little bit, probably, possibly up above the knees.” However, according to Licata, the upper half of the victim’s dress “was definitely buttoned up all the way to the top. There was nothing that seemed obviously ripped or torn.”
Licata determined that the victim was dead. During his examination, he unbuttoned the victim’s dress only as far as necessary to apply two “paddles” of a heart monitor. He did not force open or rip the dress; he did not touch the lower half of the victim’s dress. Licata was the only paramedic that touched the victim.
At approximately 6 p.m., Schaumburg police department supervisor Thomas Fries and Lieutenant Winkelhake arrived at the apartment complex in response to a police call. After searching the victim’s *442apartment and telephoning the department, Officer Fries and other officers canvassed the neighborhood for any potential witnesses.
Officer Fries went to defendant’s apartment and knocked on the door. He observed the door’s peephole become dark, and then light again. Fries knocked again and announced his office. He continued to knock and announce his office intermittently for the next 15 minutes, until detectives arrived.
When Sergeant Barr arrived, Officer Fries briefed him on the events leading up to his (Fries’) observations at defendant’s door. Sergeant Barr then knocked on defendant’s door. Barr and Fries saw the peephole again become dark and then light. Officer Fries sent additional patrolmen to the other side of defendant’s apartment.
At around 6:30 p.m., Schaumburg Police Detective Martin Friel arrived at the apartment complex. Police officers briefed Detective Friel on the shadows seen from the peephole of defendant’s apartment door. Friel located the building management, who told him that Vanessa Allen was the record tenant of the apartment.
Detective Friel telephoned Allen at work. She told Friel that she lived in the apartment alone. She also told Friel that the only other person with a key to her apartment was her brother. Based on this information, Friel told police that no one was supposed to be in the apartment.
By approximately 7:40 p.m., the police had not yet gained entry into defendant’s apartment. At that time, police saw smoke coming out from underneath the front door of defendant’s apartment.
Detective Friel went to the rear of defendant’s apartment and tried to look into defendant’s bedroom, through the separation in the bedroom window curtains. While he stood there, the curtains quickly went up in flames. Friel thereafter had an unobstructed view of *443defendant’s bedroom. Friel saw two fires burning in the bedroom. Friel then looked through a sliding glass door and saw at least three fires burning in the living room.
Schaumburg fire fighters arrived at the apartment complex. Two or three fire fighters made their way to defendant’s bedroom window. They broke out the window, extended a firehose into the apartment, and began to extinguish the fires.
Defendant attempted to exit through the bedroom window and was arrested by police. At the time of his arrest, defendant’s left hand was bleeding profusely.
Defendant, accompanied by Officer Stachnik, was taken to a local hospital. There, a nurse removed a wristwatch from defendant and gave it to Stachnik. Defendant’s hand had a deep laceration that cut through the tendons of three fingers. The hand had a second cut at the web part of the hand. The physician described the deep cut as sharp and clean, and opined that it was made by an instrument such as a knife.
At the apartment complex, police had searched the victim’s apartment. Evidence technician James Herman determined from the pattern of spattered blood in the kitchen that there was a large amount of blood from someone other than the victim. He collected blood samples from various areas in the apartment. He saw the two piles of the white substance that appeared to him to be sugar. He took a sample from the pile near the vacuum, but did not test the pile near the door.
Acting on a search warrant, police searched defendant’s apartment. Evidence technician Herman saw evidence of six fires in the living room and six more in the bedroom. Each fire was fueled by a little pile of items. In the living room, there were several piles of bedding and pillows, clothing, and several household items. Herman was directed to a satchel bag, inside of which was a coffee cup. Inside the cup was a substance that *444appeared to be sugar and, on the bottom of the cup, there appeared to be blood. In the bedroom, there were several separate plastic bags of clothing that burned independently of each other. They had not completely burned by the time the fires were extinguished. In one of the piles was a wallet that contained defendant’s driver’s license, and a knife with a stained wooden handle.
Tests of the white substance recovered from the victim’s apartment near the vacuum cleaner revealed that it was sugar. The white substance inside the coffee cup found in defendant’s apartment was also sugar.
The victim’s blood was determined to be type AB, while defendant’s blood was type A. Blood samples taken from several locations in the victim’s apartment all were of defendant’s blood type. Additionally, blood was found on defendant’s wristwatch and on his knife. The blood on the wristwatch and knife was the blood type of the victim.
Lastly, an autopsy revealed that the victim died of multiple stab wounds. The autopsy also revealed that the victim suffered defense wounds to the hands and arms. Although the wounds could possibly have been made by defendant’s knife, they could not be tied to any particular weapon.
Defendant’s evidence at trial was essentially as follows. On the morning of May 18, 1988, defendant was ill and did not go to work. Allen made a cup of tea with sugar for defendant. When she left for work at 10:45 a.m., the cup was on the floor. Defendant identified the cup as the same cup police found in the satchel. However, defendant denied putting the cup in the bag.
In the early afternoon, defendant took over-the-counter medication for his illness, which made him drowsy. At approximately 3 p.m., defendant’s sister visited defendant for about 20 minutes. After she left, defendant fell asleep. When he awoke, he carried a bas*445ket of clothes to the laundry on the building’s second floor, put the clothes in a washing machine, and returned directly to his apartment.
At approximately 4 p.m., defendant removed a package of frozen pork chops from his freezer and placed it in his kitchen sink under hot running water. Defendant then removed the package from the water, cut the wrapper, and tore open the package. Defendant, who is left-handed, then held the still-frozen chops in his left hand and attempted, with his right hand, to pry them apart with a sharp kitchen knife. The knife slipped and defendant inflicted a minor cut on his left hand. Defendant tried a second time to separate the chops. The knife slipped again and defendant inflicted a deep, bloody wound on his left hand.
Defendant held the wounded hand under running water, and tightly wrapped a towel around the hand to stop the bleeding. He wrapped the hand in a bedsheet, took Tylenol to relieve the pain, lay down, and fell asleep.
Defendant awoke to his telephone ringing and pounding on his front door. Defendant looked through the door’s peephole and saw police. He did not respond because he did not want the building management to learn that he was there. He was not a tenant and, therefore, feared that he and Allen would lose their security deposit.
Defendant telephoned Allen and told her about his hand. Allen told defendant that she and her mother would come to him and take him to a hospital. He watched television for awhile and then went to the bathroom to run cold water on the cut. The bathroom door was closed at the time.
Defendant heard glass breaking. When he opened the bathroom door, he saw smoke and fire. He closed the bathroom door and turned on the bathroom exhaust fan. Defendant then heard his front door being kicked. Ap*446proximately 15 minutes later, defendant left the bathroom and exited the apartment through the smashed bedroom window.
During the State’s cross-examination of defendant, the State confronted defendant with a photograph of an unopened package of pork chops lying on defendant’s kitchen counter. The unopened package was introduced into evidence. Defendant also could not explain when asked why the knife handle appeared to be covered with blood if only the blade had touched his hand.
Defendant denied that he set the fires in his apartment. Defendant believed that the police broke into his apartment and set the fires to force him to come out. Defendant denied placing the knife in a pile of burning clothes. He believed that police put the knife and wallet in the burning pile because he was the most convenient suspect, and also because of “the prejudice in the northwest suburbs.”
At the close of the evidence and argument, the jury convicted defendant of first degree murder, aggravated arson, home invasion, and armed violence.
Defendant waived a sentencing jury. In the first phase of the sentencing hearing, the trial judge found the presence of an aggravating factor: the murder was committed in the course of a felony, i.e., home invasion. Thus, the trial judge concluded that defendant was eligible for the death penalty.
During the second stage of the sentencing hearing, the State presented evidence in aggravation and defendant presented evidence in mitigation. At the close of the sentencing hearing, the trial judge found that death was an appropriate sentence for defendant and that there were no mitigating factors sufficient to preclude imposition of the death penalty. Thus, the trial court sentenced defendant to death on the first degree murder conviction. The trial judge found that the armed violence con*447viction merged into the first degree murder conviction. The trial judge also sentenced defendant to concurrent 30-year prison terms on the aggravated arson and home invasion convictions.
Defendant appeals. Additional relevant facts will be discussed in the context of the issues raised on appeal.
Concerning pretrial procedures, defendant contends: (1) the Cook County jury selection system deprived him of his constitutional rights; (2) the trial judge deprived defendant of his constitutional rights by refusing to ask all venirepersons questions tendered by defendant concerning racial prejudice, and refusing to question two particular venirepersons on that subject; (3) the trial judge deprived defendant of a fair trial by excusing for cause particular venirepersons and not others; and (4) the State denied him a fair trial by using a challenge for cause and a peremptory challenge to exclude two black venirepersons from the jury.
Constitutionality of Venire Selection
Defendant was tried in Rolling Meadows, a northwest suburb of Chicago, located in the third municipal district of the circuit court of Cook County (third district). Defendant filed a pretrial motion to dismiss the jury venire. (See Ill. Rev. Stat. 1987, ch. 38, par. 114 — 3.) He claimed that Cook County jury selection procedures result in systematic underrepresentation of African-Americans in third district venires.
Section 9.2 of the Jury Commission Act (Act) provides that, in single-county judicial circuits that contain more than one million inhabitants, jurors may be drawn from such parts of the county as are determined by *448court rule to be most favorable to an impartial trial and to not incur unnecessary expense or unduly burden the citizens. Ill. Rev. Stat. 1987, ch. 78, par. 32.2.
Cook County Circuit Court Rule 0.4 (Cir. Ct. Cook County R. 0.4 (eff. July 1, 1976)) implements this statutory provision. Rule 0.4(c) divides Cook County into three parts. Part I is composed of the entire county. Part II is composed of postal zip code areas which constitute the northern half of the county. Part III is composed of postal zip code areas which constitute the southern half of the county. Roosevelt Road in Chicago is the dividing line between the two halves. Venirepersons are summoned to jury service to a facility within that part of the county from which their names were drawn. Venirepersons for the third district of the Cook County circuit court are drawn from the northern half of the county.
Defendant presented the testimony of two witnesses in support of his motion to dismiss the venire. James Digby was the jury supervisor for the third district. Defendant presented Digby’s testimony in an offer of proof. Digby testified as follows. Venires for the third district are called from the prescribed area, and geography is the only factor in designating jurors for the Rolling Meadows courthouse.
From February through December of 1989, Digby recorded the racial composition of third district venires based on his observations. On the day of his testimony, 52 venirepersons reported for jury service; he observed that 5 were black, while 47 were “white and other.” On the next day, 47 venirepersons reported for jury service; Digby observed that 1 was black, while 46 were “white and other.”
Paul Kleppner, director of the Social Science Research Institute at Northern Illinois University, also testified in support of defendant’s motion. Kleppner compared Cook County registered voters who live in *449northern Cook County with those who live in southern Cook County, with the dividing line at Roosevelt Road in Chicago.
According to Kleppner’s statistical analysis, almost exactly half of Cook County’s registered voters live in each half of the county. Also, 26% of all Cook County registered voters are black, while 70.4% are white.
However, only 25.4% of the county’s black registered voters live in the northern half of the county, while 75.4% live in the southern half. As a result, focusing on the northern half of the county, only 12.6% of the registered voters are black, while 82.9% are white. In contrast, in the southern half of the county, 39.9% of the registered voters are black, while 57.6% are white. Kleppner concluded that a venire that was randomly drawn from the northern half of Cook County would be expected to contain only half as many black venirepersons as a venire drawn from Cook County as a whole.
The trial judge excluded Digby’s tabulations from evidence. However, the trial judge considered the statistics propounded by Kleppner to be reliable.
The trial judge denied defendant’s motion to dismiss the venire. The judge found that defendant did not show that: (1) a distinct group in the community was unfairly and unreasonably represented in third district venires, or (2) Rule 0.4 systematically excluded that group from the venire. The trial judge also denied defendant’s motion to poll the venire to ask venirepersons how they were assigned to the Rolling Meadows courthouse.
Defendant claims that Rule 0.4 results in the systematic underrepresentation of African-Americans in third district venires. Defendant bases his claim on the sixth and fourteenth amendments to the United States Constitution, and on the Illinois Constitution. We note that defendant has not cited authority or provided argument for his claim of unconstitutionality based on the Illinois *450Constitution. Thus, we deem the point to be waived. (134 Ill. 2d R 341(e)(7); People v. Dinger (1990), 136 Ill. 2d 248, 254.) However, we agree with the trial judge that defendant failed to show that the venire was unconstitutionally selected.
The sixth amendment to the United States Constitution requires that a petit jury be drawn from a fair cross-section of the community. (U.S. Const., amend. VI; Taylor v. Louisiana (1975), 419 U.S. 522, 528, 42 L. Ed. 2d 690, 697, 95 S. Ct. 692, 697.) The United States Supreme Court recently explained that “[t]he Sixth Amendment requirement of a fair cross section on the venire is a means of assuring, not a representative jury (which the Constitution does not demand), but an impartial one (which it does).” (Emphasis in original.) Holland v. Illinois (1990), 493 U.S. 474, 480, 107 L. Ed. 2d 905, 916, 110 S. Ct. 803, 807.
To establish a prima facie violation of the fair-cross-section requirement, a defendant must show that: (1) the group allegedly excluded is a distinctive group in the community; (2) the underrepresentation of that group in venires, from which juries are selected, is not fair and reasonable in relation to the number of such persons in the community; and (3) the underrepresentation is due to the systematic exclusion of that distinctive group in the jury selection process. (Duren v. Missouri (1979), 439 U.S. 357, 364, 58 L. Ed. 2d 579, 586-87, 99 S. Ct. 664, 668; People v. Flores (1990), 193 Ill. App. 3d 501, 506-07.) The defendant need not be a member of the allegedly excluded group to raise a fair-cross-section challenge to the venire. Also, no evidence of intent to discriminate is required. Flores, 193 Ill. App. 3d at 507 (and cases cited therein).
If the defendant establishes a prima facie case, the burden shifts to the State to demonstrate that a significant State interest justifies the selection process which *451results in the underrepresentation. Mere rational grounds or administrative convenience will not suffice. Duren, 439 U.S. at 367-68, 58 L. Ed. 2d at 589, 99 S. Ct. at 670; Flores, 193 Ill. App. 3d at 507.
In the present case, the trial judge found that defendant met the first element of the Duren prima facie case. The State concedes that African-Americans constitute a distinct group in the community. See People v. Sledge (1989), 183 Ill. App. 3d 1035, 1044; People v. Broadnax (1988), 177 Ill. App. 3d 818, 828.
However, the trial judge found that defendant failed to establish an unfair and unreasonable underrepresentation of a distinct group in the community in third district venires. On appeal, defendant initially claims that the “community” to which we should refer is the whole of Cook County, and not only the northern half of the county, as provided by Rule 0.4.
We disagree. In Davis v. Warden, Joliet Correctional Institution at Stateville (7th Cir. 1989), 867 F.2d 1003, the United States Court of Appeals for the Seventh Circuit noted that “[c]ounty lines or federal district lines do not magically determine the parameters of a community.” (Davis, 867 F.2d at 1009.) The Davis court held that the sixth amendment does not prevent a legislature from delineating a smaller area, than the “district” wherein the crime was committed, from which to draw a jury. (Davis, 867 F.2d at 1007.) The Davis court specifically agreed with our appellate court that “ ‘[djividing a county into parts and drawing jury venires from one part of the county for cases at one court facility and from another part for cases at another facility does not per se ... deny defendants an impartial trial.’ ” (Davis, 867 F.2d at 1012, quoting People v. Johnson (1987), 154 Ill. App. 3d 301, 306.) Thus, courts treat “the community in jury selection challenges as coextensive with the *452geographic area from which the court or legislature ordered the venire drawn.” Davis, 867 F.2d at 1010.
Based on this legislative power, a court “should not redefine the area from which the legislature has ordered the jury list to be drawn without a lawful justification.” (Davis, 867 F.2d at 1009.) The Davis court specifically noted that Rule 0.4 conformed with the court’s holding that State employees and venirepersons maintain the “community” as designated by existing jury selection rules promulgated by the legislature or implemented by a court. Davis, 867 F.2d at 1009 n.8.
In the case at bar, defendant resided, committed his crimes, and was tried in the northern half of Cook County. Pursuant to statute, implemented by Rule 0.4, venires for defendant’s trial at the Rolling Meadows courthouse were drawn from the northern half of Cook County. In terms of the second element of the Duren prima facie case, we hold that the “community” to which we refer is the northern half of Cook County and not the county as a whole.
After carefully reviewing the record, we conclude that defendant did not establish that African-Americans are unfairly and unreasonably underrepresented in third district venires in relation to their number in the northern half of Cook County. Digby testified that he recorded the racial composition of venires based on his observations at the Rolling Meadows courthouse between February and December 1989. However, defendant did not present any foundation for their accuracy or validity. For example, Digby did not testify that he observed every venire at the courthouse. Further, eight business days were missing from the tabulations. Lastly, Digby identified the race of venirepersons based on his personal observations, without any degree of scientific certainty. We note that the appellate court has considered far more evidence than presented here to have not been sufficient to *453establish a Duren prima facie case. See Broadnax, 177 Ill. App. 3d at 823-25, 829-30.
Further, Digby’s tabulations do not establish an unfair or unreasonable underrepresentation of African-Americans in third district venires when compared to their number in the northern half of Cook County. Kleppner’s statistics showed that 12.6% of the registered voters in the northern half of Cook County were African-American. In comparison, Digby’s tabulations indicated that, from February to December 1989, 10.14% of the venirepersons reporting for jury service were African-American. The disparity that results from this comparison, 2.46%, is not sufficient to demonstrate an unfair or unreasonable underrepresentation of African-Americans on third district venires. (Compare, e.g., Duren, 439 U.S. at 362-63, 58 L. Ed. 2d at 585-86, 99 S. Ct. at 667-68 (39.5%); Taylor, 419 U.S. at 524, 42 L. Ed. 2d at 694, 95 S. Ct. at 695 (43%).) We hold that defendant failed to establish the second element of a Duren prima facie case.
We additionally note that defendant failed to establish the third element of a Duren prima facie case. We agree with the trial judge that defendant failed to show that Rule 0.4 systematically excluded African-Americans from the venire. Defendant’s own witness, Digby, testified that geography was the only factor in designating juries to the Rolling Meadows courthouse. Also, section 2 of the Act expressly authorizes the selection of venires based on voter registration lists. (Ill. Rev. Stat. 1987, ch. 78, par. 25.) We agree with the appellate court that “[u]sing voter registration lists to select persons to serve on juries is facially neutral, as it allows no opportunity for subjective or racially motivated judgments.” (People v. Saunders (1989), 187 Ill. App. 3d 734, 744.) We hold that defendant failed to establish a prima facie case of a *454violation of his sixth amendment right to a fair cross-section of the community on the venire.
Defendant based his written motion to dismiss the venire also on the equal protection clause of the fourteenth amendment to the United States Constitution. (U.S. Const., amend. XIV.) The equal protection clause requires that the selection of both grand and petit jurors be free from any taint of discriminatory purpose. Flores, 193 Ill. App. 3d at 509, citing Strauder v. West Virginia (1880), 100 U.S. 303, 25 L. Ed. 664; People v. Rosa (1982), 111 Ill. App. 3d 384, 387-88 (and cases cited therein).
To establish a prima facie case of an equal protection violation, a defendant must establish: (1) that the group to which he belongs is one that is a recognizable class of persons capable of being singled out for discriminatory treatment; (2) substantial underrepresentation of that recognizable class of persons over a significant period of time; and (3) a discriminatory purpose in such under-representation, which may be shown either by the strength of the statistical showing, known as the rule of exclusion, or by showing a selection procedure that is susceptible of abuse or is not racially neutral. Castaneda v. Partida (1977), 430 U.S. 482, 494-95, 51 L. Ed. 2d 498, 510-11, 97 S. Ct. 1272, 1280; Flores, 193 Ill. App. 3d at 509-10.
Once the defendant establishes a prima facie case of an equal protection violation, the burden shifts to the State to rebut the presumption of unconstitutional action by showing that permissible racially neutral criteria and procedures were employed. Flores, 193 Ill. App. 3d at 510.
The State concedes that defendant has established the first element of an equal protection violation. However, we agree with the State that defendant has failed to establish the second and third elements: a substantial *455underrepresentation over a significant period of time, and a discriminatory purpose.
As we noted earlier, according to Digby’s tabulations, the statistical disparity between African-Americans residing in the northern half of Cook County and those in third district venires was 2.46%. We do not consider a statistical disparity of 2.46% to constitute a substantial underrepresentation, or proof of a discriminatory purpose. (See Broadnax, 177 Ill. App. 3d at 830-31.) As we also noted earlier, Digby recorded his observations from February to December 1989, a period of only approximately 11 months. We do not consider this to be a significant period of time. (See Flores, 193 Ill. App. 3d at 510-11.) Lastly, the use of voter registration lists is a facially neutral procedure. (Saunders, 187 Ill. App. 3d at 744.) We hold that defendant failed to establish a prima facie case that he was denied the equal protection of the laws. Thus defendant failed to establish that the venire was unconstitutionally selected.
Defendant next contends the trial judge should have considered Digby’s testimony in ruling on the motion to dismiss the venire. The judge noted that Digby based his tabulations solely on his observations, “the observation[s] of one man only, without any input from the people being observed.” The trial judge found that Digby based his tabulations on his “subjective, unscientific” observations. The judge concluded that Digby’s tabulations were incompetent and, therefore, inadmissible.
In Illinois, however, all relevant evidence is admissible, unless otherwise provided by law. (People v. Monroe (1977), 66 Ill. 2d 317, 321, quoting People ex rel. Noren v. Dempsey (1957), 10 Ill. 2d 288, 293; M. Graham, Cleary & Graham’s Handbook of Illinois Evidence §402.1 (5th ed. 1990).) Relevancy is established where what is offered as evidence has any tendency to make the existence of any fact in consequence to the determination of *456the action more or less probable than it would be without the evidence. Monroe, 66 Ill. 2d at 321-22 (and authorities cited therein); People v. Jones (1982), 108 Ill. App. 3d 880, 884.
It is true that a trial court may reject proffered evidence on grounds of irrelevance if the evidence has little probative value due to its remoteness, uncertainty, or possibly unfair prejudicial nature. (People v. Ward (1984), 101 Ill. 2d 443, 455.) However, “[t]he concept of relevancy must be kept separate from any issue as to sufficiency of evidence.” (M. Graham, Cleary & Graham’s Handbook of Illinois Evidence §401.1, at 129 (5th ed. 1990).) Additionally, the admission of evidence lies within the sound discretion of the trial court, and its ruling should not be reversed absent a clear abuse of that discretion. Ward, 101 Ill. 2d at 455-56.
Applying these principles to the present case, we conclude that Digby’s testimony regarding his tabulations of jury venire composition in the third district was relevant and, therefore, admissible. In other words, Digby’s tabulations tended to make the issue of systematic under-representation of black venirepersons in third district venires more or less probable.
The State contends that Digby’s tabulations were not admissible because Digby was not a statistician, and because his tabulations were incomplete and inaccurate. However, these arguments go to the weight of the evidence and not its admissibility. (See M. Graham, Cleary & Graham’s Handbook of Illinois Evidence §401.1, at 129 (5th ed. 1990).) Digby’s tabulations were not so remote or uncertain as to render them irrelevant and inadmissible.
We note that, in the context of a Batson hearing (see Batson v. Kentucky (1986), 476 U.S. 79, 90 L. Ed. 2d 69, 106 S. Ct. 1712), the testimony of trial counsel is relevant evidence of the number of peremptory strikes *457against black venirepersons (People v. Andrews (1992), 146 Ill. 2d 413, 429). If the testimony of trial counsel, based on observation, is relevant evidence of purposeful discrimination in the exercise of peremptory challenges, then Digby’s tabulation, based on observation, is relevant evidence of underrepresentation in the composition of third district venires. We hold that the trial judge should have considered Digby’s testimony in ruling on defendant’s motion to dismiss the venire. However, although Digby’s tabulations wefe admissible evidence, we conclude that their admission would not have changed the trial judge’s conclusion that the venire was not unconstitutionally selected.
Defendant contends the trial judge erred by refusing to poll the venire to ask venirepersons how they were assigned to the Rolling Meadows courthouse. In his appellate brief, defendant explains that he had the right to find evidence of whether venirepersons in the third district were actually selected according to Rule 0.4. However, the record shows that defendant did not explain his request to the trial judge in an offer of proof. Rather, defendant merely made the motion, which the trial judge denied.
When a trial court refuses evidence, no appealable issue remains unless a formal offer of proof is made. (People v. Montgomery (1977), 51 Ill. App. 3d 324, 331.) The purpose of an offer of proof is to inform the trial court, opposing counsel, and a reviewing court of the nature and substance of the evidence sought to be introduced. (Volvo of America Corp. v. Gibson (1980), 83 Ill. App. 3d 487, 491; People v. Rosa (1977), 49 Ill. App. 3d 608, 613.) Where it is not clear what a witness would say, or what his basis would be for saying it, the offer of proof must be considerably detailed and specific. A reviewing court can thereby know what was excluded and determine whether the exclusion was proper. (Volvo, 83 Ill. *458App. 3d at 491; Rosa, 49 Ill. App. 3d at 614 (both quoting Hession v. Liberty Asphalt Products, Inc. (1968), 93 Ill. App. 2d 65, 71).) “The failure to make an adequate offer of proof results in a waiver of the issue on appeal.” People v. Andrews (1992), 146 Ill. 2d 413, 421.
However, an offer of proof is not required where it is apparent that the trial court clearly understood the nature and character of the evidence sought to be introduced, or where the question itself and the circumstances surrounding it show the purpose and materiality of the evidence. Volvo, 83 Ill. App. 3d at 491; Montgomery, 51 Ill. App. 3d at 331.
After carefully reviewing the record, we conclude that it was by no means clear what testimony the venirepersons would have provided, and what would have been the basis for their testimony. Further, Digby, defendant’s witness, testified that geography was the only factor in assigning jurors to the Rolling Meadows courthouse. Defendant did not relate any contrary suspicions to the trial judge. Thus, we cannot say that the trial judge clearly understood why defendant sought to have venirepersons asked how they were assigned to that courthouse. The failure to make an offer of proof precludes this court from knowing what the venirepersons’ evidence would have been. Therefore, we cannot review any alleged error in its exclusion. See Andrews, 146 Ill. 2d at 421-22; Montgomery, 51 Ill. App. 3d at 332.
Questioning the Venire
Defendant next claims that the trial judge deprived him of his constitutional rights to a fair trial by refusing to ask all venirepersons questions tendered by defense counsel concerning racial prejudice, and to question two particular venirepersons on that subject.
It is settled that a litigant has a basic constitutional right to a trial by an impartial jury. However, that right *459does not require that the litigants themselves be permitted to question the jurors. “Examination of prospective jurors by court or by counsel is not a part of the right to trial by jury but, rather, a matter of trial detail which courts can regulate in the exercise of judicial discretion.” (People v. Jackson (1977), 69 Ill. 2d 252, 260.) We agree with the appellate court that the test for evaluating the court’s exercise of discretion is whether the means used to test impartiality have created a reasonable assurance that prejudice would be discovered if present. People v. Bunch (1987), 159 Ill. App. 3d 494, 510; People v. DeSavieu (1983), 120 Ill. App. 3d 420, 427.
Prior to voir dire, defense counsel tendered two lists of questions to ask all venirepersons. Three of the questions on one list pertained to the venirepersons’ potential for racial prejudice where the defendant was black and the victim was white.
The trial judge refused to ask the three questions that specifically pertained to race. The judge did not believe that special circumstances existed that suggested a significant likelihood that racial prejudice would infect defendant’s trial. Rather, the trial judge believed that asking the questions would inject the subject of race into the trial when it was previously absent.
It is the duty of the trial court to manage the voir dire. (DeSavieu, 120 Ill. App. 3d at 427.) Thus, the decision to permit supplemental questions by counsel in a voir dire examination is within the discretion of the trial court. Bunch, 159 Ill. App. 3d at 510; DeSavieu, 120 Ill. App. 3d at 427.
Further, during voir dire, the Constitution requires a trial judge to question venirepersons specifically regarding racial prejudice if “special circumstances” exist that suggest a constitutionally significant likelihood that racial prejudice might infect a defendant’s trial. Such circumstances exist where racial issues are “inextricably *460bound up with the conduct of the trial.” Ristaino v. Ross (1976), 424 U.S. 589, 596-97, 47 L. Ed. 2d 258, 264, 96 S. Ct. 1017, 1021, explaining Ham v. South Carolina (1973), 409 U.S. 524, 35 L. Ed. 2d 46, 93 S. Ct. 848; see Rosales-Lopez v. United States (1981), 451 U.S. 182, 189, 68 L. Ed. 2d 22, 29, 101 S. Ct. 1629, 1635 (opinion of White, J.).
However, “[tjhere is no constitutional presumption of juror bias for or against members of any particular racial or ethnic groups.” (Rosales-Lopez, 451 U.S. at 190, 68 L. Ed. 2d at 29, 101 S. Ct. at 1635 (opinion of White, J.).) The sole fact that the defendant is black and the victim is white “does not constitute a 'special circumstance’ of constitutional proportions.” Turner v. Murray (1986), 476 U.S. 28, 33, 90 L. Ed. 2d 27, 35, 106 S. Ct. 1683, 1687 (opinion of White, J.); see Rosales-Lopez, 451 U.S. at 190, 68 L. Ed. 2d at 29, 101 S. Ct. at 1635 (opinion of White, J.); Ristaino, 424 U.S. at 597, 47 L. Ed. 2d at 265, 96 S. Ct. at 1022.
Applying these principles to the present case, we conclude that the trial judge did not err in refusing defense counsel’s tendered questions. The trial judge asked each venireperson whether sympathy, bias, or prejudice would affect his or her judgment. Thus, defendant was given sufficient opportunity to discover any bias or prejudice held by jurors. See Bunch, 159 Ill. App. 3d at 510.
We further conclude that the “special circumstances” described in Ristaino do not exist in the present case. The only fact of record to which defendant can point is that he is black and the victim is white. See People v. Diaz (1984), 123 Ill. App. 3d 239, 242-43.
Also, it is true that “a capital defendant accused of an interracial crime is entitled to have prospective jurors informed of the race of the victim and questioned on the issue of racial bias.” (Turner, 476 U.S. at 36-37, 90 L. Ed. 2d at 37, 106 S. Ct. at 1688.) However, the “special *461circumstance” in such a case does not come into play at the guilt phase of the trial, but rather at the sentencing phase. (Turner, 476 U.S. at 38 n.12, 90 L. Ed. 2d at 37 n.12, 106 S. Ct. at 1689 n.12 (opinion of White, J.).) In the present case, since defendant waived a sentencing jury, this special circumstance is not present. We cannot say that the trial judge abused his discretion in refusing to ask all venirepersons the disputed voir dire questions.
Defendant further claims that the trial judge deprived him of his constitutional rights by refusing to question two particular venirepersons, Kasimir Wismont and Jose Ortiz, on the subject of racial prejudice. During voir dire, Wismont told the trial judge that, in 1975, his wife was robbed and beaten at a rapid transit station on the Eisenhower Expressway at Cicero Avenue.
However, in response to the trial judge’s questions, Wismont indicated that he did not have any preconceived notions in this case for or against one side or the other, and that he could be fair to both sides. Wismont further indicated that he understood and believed that the State carried the burden of proving guilt beyond a reasonable doubt, and that defendant was not required to testify.
After the trial judge’s examination of Wismont, defense counsel requested the judge to ask Wismont whether his wife’s attackers were black and whether he harbored any ill will toward blacks. The trial judge denied the request, explaining that such questions would inject race into the trial.
Ortiz told the trial judge that, two years prior to voir dire, a 16-year-old nephew had been murdered because he was mistaken for another. However, in response to the trial judge’s questions, Ortiz indicated that he understood the presumption of innocence, the right of a defendant not to testify, and the State’s burden of proof beyond a reasonable doubt. Ortiz also indicated that: he *462could be fair to both sides; he had no bias or prejudice for or against either side in the case; and the murder of his nephew did not create any bias or prejudice for or against either side.
After the trial judge’s examination of Ortiz, defense counsel requested the judge to ask Ortiz the race of his nephew’s killers. The trial judge denied the request.
After carefully reviewing the record, we conclude that the trial judge’s voir dire examination of Wismont and Ortiz gave defendant sufficient opportunity to discover any bias or prejudice held by them. The trial judge’s general questions focused the attention of Wismont and Ortiz on the specific areas of potential prejudice. This was a sufficient test for impartiality. (See People v. Partee (1987), 157 Ill. App. 3d 231, 259.) We cannot say that the trial judge abused his discretion in refusing to question venirepersons Wismont and Ortiz on the subject of race.
Excusal of Venirepersons for Cause
Defendant next claims that the trial judge deprived him of a fair trial by excusing for cause three venirepersons, Derrick Blakely, John Molcan, and Elizabeth Sellars, and refusing to excuse for cause one venireperson, Anthony Incando.
Of course, the right to a jury trial guarantees to a criminal defendant a fair trial by a panel of impartial jurors. (People v. Cole (1973), 54 Ill. 2d 401, 411.) Impartiality is not a technical concept. Rather, impartiality is a state of mind, or a mental attitude. (Cole, 54 Ill. 2d at 413.) A venireperson’s state of mind must be ascertained from statements made by the venireperson, given the weight to which they are entitled under the circumstances. (People v. Leger (1992), 149 Ill. 2d 355, 385, citing Cole, 54 Ill. 2d at 414; People v. Partee (1987), 157 Ill. App. 3d 231, 257.) Further, the judge should consider *463the venireperson’s entire voir dire examination, and not single out certain statements. (People v. Stone (1978), 61 Ill. App. 3d 654, 667.) A person is not competent to sit as a juror if his state of mind or mental attitude is such that, with him as a member of the jury, the defendant will not receive a fair and impartial trial. (Cole, 54 Ill. 2d at 413.) We note that the function of voir dire is to secure an impartial jury. It was not designed to enable a defendant to select particular jurors. People v. Lobb (1959), 17 Ill. 2d 287, 301.
The burden of showing that a venireperson possesses a disqualifying state of mind is on the party making the challenge. (Cole, 54 Ill. 2d at 413.) The determination of the juror’s qualification must be made from the evidence; mere suspicion of bias is not evidence. (Cole, 54 Ill. 2d at 415.) The determination of whether or not the venireperson has the state of mind which will enable him to give to an accused a fair and impartial trial rests in the sound discretion of the trial judge. His determination should not be set aside unless it is against the manifest weight of the evidence. Cole, 54 Ill. 2d at 414-15.
Derrick Blakely was a news reporter for a Chicago television station. During the trial judge’s initial examination, Blakely generally stated that he could be fair and impartial. Blakely was, thereafter, further questioned in chambers. Blakely stated that he had met most reporters from his or other stations. In response to the trial judge’s questions, Blakely stated: “Probably am sympathetic to journalists. I would think so, but beyond that, I can’t say.”
News videotapes, with the accompanying testimony of reporters or cameramen, could possibly have been offered as evidence at trial. Blakely expressed self-doubt as to his ability to be impartial regarding journalist testimony. Thus, Blakely was not prepared to stand indifferent, and to be guided only by law and the evidence. (See *464 People v. Hobbs (1966), 35 Ill. 2d 263, 270.) We hold that the trial court’s excusal of Blakely was not against the manifest weight of the evidence.
On February 22, 1990, John Molcan, and on February 23, Elizabeth Sellars, each reported seeing a newspaper article on the crime. Each stated that the article reported that defendant had waived his right to a sentencing jury. On the preceding day, the trial judge instructed the venirepersons that if any of them inadvertently happened to be exposed to media coverage of the case, he or she should immediately report the fact to the court. The trial judge excused Molcan and Sellars.
In People v. Lucas (1989), 132 Ill. 2d 399, this court held that it is not an abuse of discretion for a trial judge to exclude venirepersons for cause where they have learned that the defendant is eligible for the death penalty but has waived a jury for sentencing. Rather, the exclusion of such venirepersons prevents the contamination of the venire and the injection of the death penalty issue into jury deliberations. This sound exercise of discretion thus avoids possible prejudice to either side and attempts to insure a fair trial. Lucas, 132 Ill. 2d at 425-26.
Defendant asks us to reconsider Lucas on this issue. We decline to do so. We hold that the trial judge’s exclusion of Molcan and Sellars was not against the manifest weight of the evidence.
Defendant contends the trial judge abused his discretion also by refusing to excuse for cause Anthony Incando. Incando told the trial judge that approximately two years prior to trial in this case, he was a juror in a Cook County murder trial. That trial proceeded to a verdict. The following colloquy occurred between Incando and the trial judge:
“Q. And did you get any notions about justice in general from sitting through that trial?
*465A. Sometimes I think he’s got his hands tied.
Q. Whose hands?
A. The State.
Q. Why do you think that?
A. Well, from what they discussed after the trial. There was a lot of things they couldn’t say.
Q. Do you think that’s wrong?
A. I have mixed emotions. In my old age, I’m getting cynical.
Q. You think we should streamline this whole process?
A. Somewhat, yes.
Q. You think the jury should be allowed to hear anything at all?
A. To an extent.
Q. A lot of people agree with you, including the judges in the federal courts. That’s basically what the rules of evidence say over there now, especially in certain cases. But you evidently have some significant doubts, I would say, about the process.
A. I have always tried to be fair.
Q. And whether or not it’s a valid process in this day and age, you don’t think it is?
A. To an extent, no.”
In response to additional questioning by the trial judge, Incando stated that he understood and believed in the presumption of innocence, and the State’s burden of proof beyond a reasonable doubt. Also, Incando unequivocally stated that he could be fair to both sides in the case.
Defendant moved to excuse Incando for cause. Defendant argued that Incando might not be fair and impartial. Defendant expressed the fear that if the State failed to meet its burden of proof, Incando would assume that evidence existed that the State could not present. The trial judge denied the motion. Defendant subsequently struck Incando from the jury with a peremptory challenge.
*466We agree with the trial judge’s ruling. Defendant’s fears of Incando’s sympathy toward the State were mere suspicions and not evidence. (See Cole, 54 Ill. 2d at 415.) In contrast, Incando unequivocally stated that he could be fair to both sides. Thus, he was prepared to stand indifferent, and to be guided only by law and the evidence. (See Hobbs, 35 Ill. 2d at 270.) We hold that the trial judge’s refusal to excuse Incando for cause was not against the manifest weight of the evidence. See People v. Johnson (1992), 149 Ill. 2d 118,136-38.
Defendant also claims that the trial judge’s discussion with Incando denied him an impartial jury. Defendant argues that the trial judge’s support of Incando’s belief, that the rules of evidence kept State’s evidence from juries, tainted the entire venire. Defendant argues that the trial judge erred by refusing to either admonish the venire to disregard the remarks, or ask venirepersons whether the remarks affected their ability to be fair and impartial.
We agree with defendant that the trial judge should not have commented on Incando’s views regarding the rules of evidence. Courts have long observed that jurors are very watchful of the trial judge’s attitude. The trial judge’s influence upon jurors is necessarily of great weight. Thus, the judge’s slightest word or intimation is received with deference and may prove controlling. In a criminal trial, the judge’s hostile attitude toward an accused or his witnesses, or expression of opinion generally, is quite apt to influence the jury in arriving at its verdict. People v. Marino (1953), 414 Ill. 445, 450-51; People v. Kelley (1983), 113 Ill. App. 3d 761, 767.
Also, from a trial judge’s use of ill-considered or ambiguous comments, which have only a tangential relationship to the issue at hand, a defendant can “imaginatively construct an argument of prejudicial error even where none truly exists.” (People v. Fort (1992), 229 Ill. App. *4673d 336, 342.) Thus, such extraneous judicial comments often result in needless appeals and a waste of judicial resources. Fort, 229 Ill. App. 3d at 342, cited in People v. Luna (1992), 234 Ill. App. 3d 544, 552.
Based on these precepts, a trial judge “should exercise restraint over his or her conduct and utterances.” (1 Standards for Criminal Justice §6 — 3.4 (2d ed. 1980).) When it becomes necessary during the trial for the judge to comment on witnesses or upon their testimony, counsel, spectators, or others, or, as in this case, upon the rules of evidence generally, the judge should do so in a restrained manner. The trial judge should: (1) avoid repartee, (2) limit his or her comments and rulings to what is reasonably required for the underlying progress of the trial, and (3) refrain from unnecessary disparagement of persons or issues, e.g., the rules of evidence. 1 Standards for Criminal Justice §6 — 3.4 (2d ed. 1980), quoted in People v. Eckert (1990), 194 Ill. App. 3d 667, 674; accord People v. Bernstein (1911), 250 Ill. 63, 67.
Although we agree with defendant that the venire should not have heard the remarks, we cannot say that the remarks prejudiced him. In People v. Erickson (1987), 117 Ill. 2d 271, and People v. Del Vecchio (1985), 105 Ill. 2d 414, remarks were heard by venirepersons that would more likely affect a jury’s impartiality than the remarks in the present case. However, this court did not consider those remarks to be so prejudicial as to preclude those juries from reaching verdicts based solely on the evidence placed before them. Erickson, 117 Ill. 2d at 292-93; Del Vecchio, 105 Ill. 2d at 428-29.
Also, it is true that the trial judge’s comments supported Incando’s view that the rules of evidence prevented a jury from hearing all of the State’s evidence. However, in his written instructions to the jury, the trial judge admonished the jury not to concern itself with the reasons for his evidentiary rulings and to disregard evi*468dence which was withdrawn or to which objections were sustained. The trial judge admonished the jury also that he did not intend, by any of his rulings or remarks during the trial, to indicate an opinion as to the evidence or what the verdict should be. We conclude that these jury instructions rendered this particular error harmless. (See People v. Wofford (1987), 156 Ill. App. 3d 238, 241-44; People v. Bradford (1979), 78 Ill. App. 3d 869, 876-77.) We cannot say that the trial judge abused his discretion in refusing to admonish or question the venire.
Defendant next claims that the State used a sham challenge for cause and a peremptory challenge to exclude two black venirepersons from the jury.
We reject at the outset defendant’s assertion that the State’s motion to exclude venireperson Blakely for cause was a sham. We earlier held that the trial judge’s ex-cusal of Blakely was not against the manifest weight of the evidence. Thus, we will focus our attention on defendant’s claim that the State used a peremptory challenge to unconstitutionally exclude venireperson Lawanda Williams. Of course, the exclusion of even one venireperson on the basis of race is unconstitutional and requires reversal of the conviction. People v. McDonald (1988), 125 Ill. 2d 182, 200.
After the jury was selected, the trial judge continued with the voir dire to select three alternate jurors. After her examination, the State peremptorily excused Williams. Defense counsel requested the trial judge to ask the prosecution to explain its exercise of the peremptory challenge. The trial judge denied the request. The judge ruled that defendant failed to establish a prima facie case of purposeful discrimination in the State’s exercise of that single peremptory challenge.
*469“The ramifications of Batson v. Kentucky (1986), 476 U.S. 79, 90 L. Ed. 2d 69, 106 S. Ct. 1712, continue to be realized.” (People v. Cannon (1992), 227 Ill. App. 3d 551, 553. See, e.g., Georgia v. McCollum (1992), 505 U.S. 42, 120 L. Ed. 2d 33, 112 S. Ct. 2348; Powers v. Ohio (1991), 499 U.S. 400, 113 L. Ed. 2d 411, 111 S. Ct. 1364.) However, Batson’s two-step procedural framework should by now be familiar; we will not repeat it here. E.g., People v. Williams (1991), 147 Ill. 2d 173, 219-20; People v. Andrews (1992), 146 Ill. 2d 413, 424; People v. Carr (1992), 225 Ill. App. 3d 170, 173.
It is settled that a Batson prima facie case cannot be established merely by the numbers of black venirepersons stricken by the State. Rather, the issue is whether this fact, in addition to “any other relevant circumstances,” raises an inference that the prosecutor conducted purposeful discrimination. People v. Holman (1989), 132 Ill. 2d 128,172-73 (and cases cited therein).
The “relevant circumstances” a trial judge may consider include, but are not limited to: whether the defendant and the excluded venirepersons share the same race; a pattern of strikes against black venirepersons; the prosecutor’s questions and statements during voir dire and in exercising his challenges; whether there has been a disproportionate use of peremptory challenges against blacks; whether the excluded blacks were a heterogeneous group sharing race as their only common characteristic; the level of black representation in the venire as compared to the jury; the race of the defendant and the victim; and the race of the witnesses. Andrews, 146 Ill. 2d at 425-26; People v. Evans (1988), 125 Ill. 2d 50, 63-64.
Additionally, a trial judge’s determination that a defendant failed to establish a Batson prima facie case is a finding of fact and will not be overturned unless it is against the manifest weight of the evidence. Andrews, *470146 Ill. 2d at 424-25; People v. Brisbon (1989), 129 Ill. 2d 200, 231.
Applying these principles to the present case, we conclude that defendant failed to establish a Batson prima facie case. The record shows that Williams was the only black venireperson the State peremptorily excused. Thus, although Williams and defendant share the same race, there was no pattern of peremptory challenges against black venirepersons. “The fact that a prosecutor exercises a peremptory challenge against a black veniremember does not, without more, demonstrate that the prosecutor engaged in purposeful discrimination in the selection of a jury.” (Carr, 225 Ill. App. 3d at 174.) This fact likewise renders neutral the factor regarding the heterogeneity of the excluded venirepersons.
Defendant, however, contends a prosecutor and the trial judge made remarks that indicated a discriminatory intent in the prosecution’s exercise of its peremptory challenges. During argument on defendant’s Batson motion, the following colloquy occurred:
“THE COURT: And it’s my duty, as a Judge, to ensure a fair jury to both sides and I think the State exercised their challenge properly; at least, as to Batson. I don’t know for whatever reasons. I haven’t heard any prima facie showing that race was involved in their exercising of the challenge.
[Prosecutor]: You know, I hate the word ‘Batson,’ because—
THE COURT: I do, too.
[Prosecutor]: —in order to show that, there has to be a showing that there was a purposeful pattern of exclusion.
THE COURT: Exactly.
[Prosecutor]: Now, how can there be when we’ve excluded no black people [with] peremptory challenges before this came up?
THE COURT: Just off the record.
*471[Prosecutor]: We don’t have to go off the record. I want this on the record, Judge.
THE COURT: I understand. I’ve ruled there’s been no prima facie showing under Batson that I would even ask you what were your reasons. I’ve already made my decision, but I’m totally at a loss here and I’m going to go off the record.”
It is unclear from this colloquy what exactly the prosecutor and the trial judge hated about the word “Bat-son.” We repeat our admonition to trial judges to avoid repartee, comments, and disparagements of persons or issues. (See Bernstein, 250 Ill. at 67; Eckert, 194 Ill. App. 3d at 674.) Further, the fact that the judge disagreed with the word “Batson” did not mean that he was tmwilling or unable to apply the Batson decision to the case before him. See People v. Hooper (1989), 133 Ill. 2d 469, 513.
Despite the brief exchange between the prosecutor and the trial judge, the record also shows that the prosecutor stated that he doubted Williams’ understanding of a defendant’s right not to testify. In response, defendant asserts that the prosecutor’s statements to this effect were pretextual. Defendant claims that white venirepersons examined during the selection of an alternate juror expressed concerns similar to Williams’, but were not peremptorily stricken by the State. However, the record does not indicate the race of those venirepersons. Thus, we cannot consider this argument. See People v. McDonald (1988), 125 Ill. 2d 182, 194-95.
Also, the State did not use a disproportionate number of peremptory challenges against black venirepersons. The record shows that the prosecution used a total of 8 peremptory challenges during voir dire, 7 during the selection of the 12 jurors and one during the selection of the 3 alternates. The prosecution exercised only one of *472these challenges, the eighth, against a black venireperson.
Additionally, we cannot consider the level of black representation in the venire as compared to the jury because the record does not indicate the final jury composition. The record also does not indicate the race of the witnesses. See McDonald, 125 Ill. 2d at 194-95.
It is true that defendant is black and the victim was white. (See People v. Henderson (1990), 142 Ill. 2d 258, 289.) However, this was only one factor out of several relevant considerations. We cannot say that the trial judge’s finding, that defendant failed to establish a Bat-son prima facie case, was against the manifest weight of the evidence.
Concerning the guilt phase of the trial, defendant contends he was denied a fair trial because the trial judge: (1) admitted into evidence irrelevant information about the victim’s church activities, misleading photographs of the victim’s corpse, and information that insinuated that a judge and a prosecutor believed defendant to be guilty; (2) refused to allow hair samples to be tested by an independent laboratory; and barred defendant from telling the jury that the State had destroyed blood samples. Defendant contends he was denied a fair trial also because the prosecutor: (3) unfairly cross-examined a defense witness; and (4) made improper and prejudicial remarks during opening statements and closing argument. Defendant also contends (5) the State failed to prove beyond a reasonable doubt an element of the offense of home invasion.
Erroneously Admitted Evidence
Defendant contends the trial judge erred by admitting into evidence irrelevant information about the vie*473tim’s church activities. Prior to trial, defendant moved to bar the State from introducing evidence that the victim was a bible teacher at her church. The State responded that the information pertained to the home invasion count. The State argued that the information was relevant to show that the victim “was a cautious person” when dealing with strangers, yet “a trusting person,” who was likely to be deceived into opening her door and admitting a stranger. The State argued that the information was relevant also to establish the time of the offense and to explain why the victim was at home at that time. The trial judge denied the motion.
Killeen testified that she met the victim through a roommate service provided by their church. The victim taught a Sunday school class and both she and Killeen regularly attended church services on Wednesday nights. Killeen knew that the victim had planned to go to church the day she was killed. Defendant contends that “[a]ll of this evidence was irrelevant and highly prejudicial.”
We conclude that the information was admissible. The information constituted character evidence, which was relevant to whether the victim would permit defendant to enter her apartment. (See, e.g., People v. Sims (1988), 121 Ill. 2d 259, 269-70.) We cannot say that the trial judge abused his discretion in admitting this evidence.
Defendant next contends the trial judge erred by admitting into evidence misleading photographs of the victim’s corpse. Defendant argues that the photographs “prejudicially insinuate a sexual assault where there was none.” The photographs show the victim lying on her back, arms outstretched, on the kitchen floor. The back of the victim’s dress was pulled up to the buttocks, while the front of the dress was pulled up to the waist, exposing her pantyhose and underwear. The photographs were taken after paramedic Licata examined the victim. Thus, the photographs show the top of the victim’s dress un*474buttoned and opened. Focusing on this sole detail, defendant assigns error to the admission of the photographs.
Photographs are properly admitted where they are relevant to establish any fact at issue, even though they may be of a gruesome nature. (People v. Lindgren (1980), 79 Ill. 2d 129, 143; People v. Speck (1968), 41 Ill. 2d 177, 202.) Photographs are admissible also where they are relevant to corroborate oral testimony on the same subject. (People v. Kubat (1983), 94 Ill. 2d 437, 495.) It is settled that “the fact that conditions had changed at the time the photographs were taken does not necessarily render them inadmissible, so long as the jury is not misled.” Warner v. City of Chicago (1978), 72 Ill. 2d 100,105.
Applying these principles to the present case, we conclude that the photographs were properly admitted into evidence. The photographs showed the cause and manner of death, explained the location and condition of the crime scene, and were relevant to corroborate the testimony of several witnesses. See Lindgren, 79 Ill. 2d at 143-44; Speck, 41 Ill. 2d at 203.
Further, the record shows that paramedic Licata carefully and thoroughly explained that when he came upon the victim, the top half of her dress was buttoned. He explained how he unbuttoned and opened the top half of the victim’s dress to examine her. Licata testified that the photographs accurately portrayed the scene in all other respects. Licata’s testimony prevented the jury from being misled by the admission of the photographs. (See People v. Grady (1982), 107 Ill. App. 3d 970, 976.) We cannot say that the trial judge abused his discretion in admitting the photographs.
Defendant also contends the trial judge erred by admitting into evidence information that insinuated that a judge and a prosecutor believed defendant to be guilty. *475Schaumburg Police Detective Edward Pope testified as follows. At approximately 9 p.m., he left the crime scene and returned to the police station, where he prepared the search warrant. In the course of preparing the warrant, Detective Pope consulted with an assistant State’s Attorney. After he completed the warrant, Detective Pope appeared before a Cook County circuit judge, who read and signed the warrant. Defendant argues that Detective Pope’s testimony, that" he consulted with the prosecutor in preparing the warrant and appeared before the judge who signed the warrant, “prejudicially insinuated to the jury that a prosecutor and a judge both believed defendant was guilty.”
Defendant concedes that he failed both to object to that portion of Detective Pope’s testimony at trial and to include the issue in his post-trial motion; thus, the issue is waived. (People v. Turner (1989), 128 Ill. 2d 540, 555; People v. Enoch (1988), 122 Ill. 2d 176, 188.) Defendant, however, asks this court to review the issue under the plain error doctrine of Supreme Court Rule 615(a) (134 Ill. 2d R. 615(a)). After reviewing the record, we conclude that this issue does not warrant our consideration under the plain error doctrine. (See People v. Myles (1985), 131 Ill. App. 3d 1034, 1046.) We cannot say that the trial judge abused his discretion in admitting this portion of Detective Pope’s testimony.
Testing of Evidence
Defendant contends the trial judge erroneously refused to allow hair samples to be tested by an independent laboratory, and barred defendant from telling the jury that the State had destroyed blood samples.
On January 5, 1990, defendant asked for a continuance to allow his forensic expert to scientifically compare hairs recovered from the victim’s left hand to samples of defendant’s hair. The hairs had not yet been tested by *476the Illinois State Crime Laboratory. The State concurred in the request for a continuance, but wanted its expert, Mohammed Tahir of the State Crime Laboratory, to test the hairs. Tahir was not available until January 22. The trial judge denied both requests for a continuance and ordered that the hairs be tested immediately by any forensic scientist at the State Crime Laboratory. However, the case was subsequently continued and Tahir became available to analyze the hair samples.
On January 29, 1990, a prosecutor informed the trial judge that Tahir had begun to analyze the hairs. However, Tahir concluded that the hair sample previously taken from defendant was unsuitable for comparison. Tahir wanted another sample from defendant consisting of 50 hairs. Defendant agreed to give the sample, but only if an independent expert, agreed upon by both sides, would test it. Defendant absolutely did not want the State Crime Laboratory to perform the analysis. The trial judge told defendant that if he wanted the analysis performed, it would have to be done by the State Crime Laboratory. Defendant responded that, based on that condition, he did not want the analysis performed.
On February 1, 1990, defendant moved that the hair samples already held by the State be turned over to defendant’s expert for testing. The trial judge denied the request, ruling that if defendant wanted the analysis done, he would have to submit a new sample to the State Crime Laboratory, where a State-employed scientist would perform the analysis. On February 26, defendant repeated this request, which the trial judge denied. As a result, the scientific comparison of the hairs found in the victim’s hand to defendant’s hair was never performed.
Defendant argues that the trial judge’s refusal to allow any testing by someone other than a scientist at the State Crime Laboratory denied him fundamental fair*477ness. “There can be no question that the defendant has a constitutional right to conduct his own tests on physical evidence.” People v. Garza (1981), 92 Ill. App. 3d 723, 734.
Supreme Court Rule 412 requires the State, upon written motion of defense counsel, to disclose to defense counsel, inter alia, any tangible object the prosecutor intends to use at trial, or which was obtained from or belongs to the defendant. (134 Ill. 2d R. 412(a)(v).) The rule further provides that the State may perform this obligation (1) in any manner agreed to by itself and defense counsel, or (2) by notifying defense counsel that those objects may be tested, and making available to defense counsel those objects “and suitable facilities or other arrangements” for the inspection and testing of those objects. 134 Ill. 2d R. 412(e).
The committee comments to Supreme Court Rule 412(e) explain as follows:
“Access to material by a defense expert must be permitted, sufficient to allow him to reach conclusions regarding the State’s examining or testing techniques and results. Where feasible, defense counsel should have the opportunity to have a test made by his chosen expert, either in the State’s laboratory or in his own laboratory using a sufficient sample.” 134 Ill. 2d R. 412, Committee Comments, at 349.
However, a defendant’s right to the independent testing of evidence is not absolute. Our appellate court correctly explained that Supreme Court Rule 412(e) does “not require an absolute transfer of custody but merely an availability that reasonably affords the defendant an opportunity to prepare his defense.” Garza, 92 Ill. App. 3d at 734.
After carefully reviewing the record, we cannot say that the trial judge failed to comply with these discovery requirements. The trial judge allowed defendant to have *478the hairs tested by any scientist at the State Crime Laboratory. Defendant refused the judge’s offer. The fact that the analysis was never performed was due to defendant’s intransigence in refusing to supply another sample of his hair. (See People v. Wright (1985), 111 Ill. 2d 128, 149-52; People v. Stinson (1976), 37 Ill. App. 3d 229, 233-34.) Ideally, the trial judge should have allowed defendant’s expert to analyze the hairs with Tahir, or at least at the State Crime Laboratory. Nevertheless, based on the facts of this case, we conclude that defendant was reasonably afforded an opportunity to prepare his defense.
On May 18, 1988, blood samples were collected from the apartments of both the victim and defendant. The samples were frozen for preservation at the State Crime Laboratory. In April 1989, a Schaumburg police officer removed the blood samples from the State Crime Laboratory and returned them to the Schaumburg police department. Tahir testified that he instructed the officer to freeze the samples. However, the police officer testified that he received instructions only regarding the package of frozen pork chops referred to earlier in this opinion. Defendant’s expert opined that the samples were unsuitable for accurate electrophoretic isoenzyme testing because they had not been properly preserved.
Prior to trial, defendant moved to bar the State from using the blood-sample evidence at trial. Defendant claimed that the police had essentially destroyed this evidence by failing to preserve it by freezing. He argued that the destruction of the evidence precluded him from performing various tests, the results of which might have exculpated him.
The trial judge denied the motion, finding, inter alia, that defendant failed to show bad faith on the part of the police. The trial judge also granted the State’s pretrial motion to bar defendant from saying during trial *479that the State had “destroyed” evidence or “permitted [the evidence] to be destroyed.” Rather, defendant could refer to the blood samples as having “deteriorated naturally.” Defendant contends the trial judge’s order denied him his constitutional right to present a defense.
In Arizona v. Youngblood (1988), 488 U.S. 51, 102 L. Ed. 2d 281, 109 S. Ct. 333, the United States Supreme Court acknowledged that the good or bad faith of the State is irrelevant when the State fails to disclose to a criminal defendant material exculpatory evidence. However, the Court continued as follows:
“But we think the Due Process. Clause requires a different result when we deal with the failure of the State to preserve evidentiary material of which no more can be said than that it could have been subjected to tests, the results of which might have exonerated the defendant. *** We therefore hold that unless a criminal defendant can show bad faith on the part of the police, failure to preserve potentially useful evidence does not constitute a denial of due process of law.” Youngblood, 488 U.S. at 57-58, 102 L. Ed. 2d at 289, 109 S. Ct. at 337.
The Court in Youngblood further held that the defendant is free to argue that the results of a particular test might have been exculpatory. However, “the police do not have a constitutional duty to perform any particular tests.” Youngblood, 488 U.S. at 59, 102 L. Ed. 2d at 290, 109 S. Ct. at 338.
After carefully reviewing the record in the present case, we uphold the trial court’s ruling that barred defendant from saying during trial that the State had destroyed the blo.od samples or permitted them to be destroyed. Defendant was still allowed to, and in fact did, present evidence that Tahir did not perform various tests on the blood samples; that the blood samples had deteriorated because the police did not freeze them for preservation; and that defendant’s expert opined that *480various tests could not accurately be performed on the blood samples due to their deterioration. Defendant also cross-examined Tahir regarding his qualifications as an expert and regarding bias. Also, defendant referred to all of these facts in his closing argument.
The right of an accused in a criminal trial to due process is essentially the right to a fair and adequate opportunity to defend against the State’s accusations. (Chambers v. Mississippi (1973), 410 U.S. 284, 294, 35 L. Ed. 2d 297, 308, 93 S. Ct. 1038, 1045; People v. Terry (1937), 366 Ill. 520, 522-23.) We hold that defendant was not denied his constitutional right to a fair opportunity to prepare a defense.
Prosecutor’s Unfair Cross-Examination
Defendant contends he was denied a fair trial also because a prosecutor unfairly cross-examined defense witness Vanessa Allen, defendant’s fiancee. Responding to the prosecutor’s questions, Allen stated that she was employed by the City of Chicago, that the city required city employees to live in the city, and that she lived in Schaumburg. The prosecutor then continued this line of questioning about the city’s residency requirement and Allen’s knowledge thereof. Allen denied any wrongdoing. Defendant argues that, by this line of questioning, the prosecutor insinuated that Allen had lied to her employer about her place of residence. Further, the prosecutor never presented evidence to substantiate the insinuation.
Although defendant objected at trial to this questioning, the record shows that he did not include the issue in his post-trial motion; thus, the issue is waived. (People v. Young (1989), 128 Ill. 2d 1, 38-40; Enoch, 122 Ill. 2d at 186.) After reviewing the record, we further conclude that this issue does not warrant our consideration under the plain error doctrine of Supreme Court Rule 615(a) (134 Ill. *4812d R 615(a)). See People v. Burns (1986), 144 Ill. App. 3d 345, 358-59.
Prosecutor’s Improper Remarks
Defendant contends he was denied a fair trial because the prosecutor, in his opening statement, mentioned the victim’s family in his introduction, stated that the evidence would show that defendant was a “human predator,” and commented on defendant’s exercise of his right to a jury trial.
A prosecutor began his opening statement in pertinent part:
“[Prosecutor]: Judge McCooey, Mr. Mermel, members of the defense, members of [the victim’s] family, members of the jury: There are human beings walking among us who can be described as human predators. The evidence in this case will show that on May 18th of 1988, William Leroy Peeples, Jr., was a human predator.
* * *
William Leroy Peeples, Jr., now stands before you, a jury of his peers, exercising his right to a jury trial on the charges of home invasion, armed violence, first degree murder and aggravated arson. He will be proved guilty beyond any shadow of a doubt to each of you and to all of you.”
Regarding the reference to the victim’s family, it is settled that “[ajrgument that the deceased left a family is improper, as it has no bearing on the guilt or innocence of the accused.” (Neal, 111 Ill. 2d at 197; see People v. Hayes (1990), 139 Ill. 2d 89, 141-42.) However, it is equally settled “that every mention of a deceased’s family does not per se entitle the defendant to a new trial. Rather, the court must consider the manner in which the references to the murder victim’s family came about.” Hayes, 139 Ill. 2d at 142.
In the present case, the prosecutor mentioned the victim’s family only once as part of a general introduction. *482The remark did not add anything to either the style or substance of the prosecutor’s argument. The remark was fleeting, and it “was not presented to the jury in such a manner as to cause it to believe that the personal characteristics of the victim or his family members were material to the defendant’s guilt or innocence.” Hayes, 139 Ill. 2d at 142-43; see Neal, 111 Ill. 2d at 197.
Regarding the prosecutor’s reference to defendant as a “human predator,” “[t]his court has repeatedly disapproved of similar remarks [citations], but has generally declined to reverse without some indication that they have resulted in substantial prejudice to the accused.” People v. Spreitzer (1988), 123 Ill. 2d 1, 39.
In the present case, the jury was at least twice instructed that opening statements are not evidence and that the jury should disregard any statement not based on the evidence. Thus, any alleged error resulting from this remark was cured. (See People v. Cunningham (1988), 177 Ill. App. 3d 544, 553; People v. Gonzalez (1980), 87 Ill. App. 3d 610, 614-15.) We do not find any substantial prejudice to defendant. See People v. Johnson (1987), 119 Ill. 2d 119, 138-42.
Regarding the prosecutor’s reference to defendant’s exercise of his right to a jury trial, defendant argues that the remark “demeaned both defendant and his constitutional right to a trial by jury.” However, the record shows that defendant did not object to the remark at trial; thus, the issue is waived. Enoch, 122 Ill. 2d at 186; Neal, 111 Ill. 2d at 196-97.
Defendant contends he was denied a fair trial also because the prosecutor made improper and prejudicial remarks during closing argument. A prosecutor has great latitude in presenting his or her closing argument. A reviewing court is reluctant to set aside a verdict based on remarks made during closing argument and does so only where the remarks are clearly prejudicial. In determining *483whether the remarks are prejudicial, a court must refer to the content of the language used, its relation to the evidence, and its effect on the rights of the accused to a fair and impartial trial. (People v. Thompkins (1988), 121 Ill. 2d 401, 445; People v. Franklin (1976), 42 Ill. App. 3d 408, 421.) Also, the trial court is in a better position than a reviewing court to determine the prejudicial effect of a remark made during closing argument. Absent a clear abuse of discretion, its ruling should be upheld. Thompkins, 121 Ill. 2d at 445-46, citing People v. Smothers (1973), 55 Ill. 2d 172,176.
Defendant contends a prosecutor made remarks that diminished the legal presumption of innocence. The remarks were as follows:
“I’d like to clear up one possible misconception that you may have had when you came into this courtroom and learned that you were going to be selected as jurors in a trial. The defendant has a right to a trial. If he chooses to exercise that right to trial, additionally he has the right to trial by a jury of his peers.
Now, he is presumed innocent throughout the entire trial unless and until from the evidence you determine that he is proven guilty beyond a reasonable doubt. But the misconception that some of you probably came into this courtroom with was: if there’s a trial, that must mean that there’s some weakness in the State’s case or there must be some real defense to this horrid crime.
Well, this trial has shown you that that is not the case. No matter how overwhelmingly the evidence is in reality as to the defendant’s guilt, he is still entitled to a trial and that’s all there is to it. There is no assumption that because there is a trial there is anything wrong with the People’s case. If he wants, he has the right to a trial and he has the right to make us bring in each and every one of the expert witnesses, prove where the items were taken from, where they were transported in sealed conditions, examined by experts, collected by experts such as Evidence Technician *484Herman, analyzed by experts such as Mohammad Tahir. He can force us to go through those steps and we have—
[Defense counsel]: I will object to that type of argument.
THE COURT: Overruled.
* * *
[Prosecutor]: *** [J]ust remember, all you have to do is look at this evidence as if you were just talking about it with somebody *** and see has it proved the defendant guilty. There should be no question in your mind at this point that it does.”
Defendant argues that the prosecutor presented motives for defendant’s proceeding to trial other than defendant’s innocence. However, the prosecutor did not present another reason for defendant’s proceeding to trial. Rather, the prosecutor remarked that defendant was presumed innocent and that the State carried the burden of proving its case. See People v. Griggs (1977), 51 Ill. App. 3d 224, 226-27, distinguishing People v. Young (1975), 33 Ill. App. 3d 443, 446-47.
Defendant argues that the prosecutor’s remarks diminished the presumption of innocence also by stating that, although defendant was entitled to certain rights or presumptions, he was not innocent. (See People v. Johnson (1986) , 149 Ill. App. 3d 465, 467.) However, “[i]t is fundamental that a prosecutor may argue that the defendant is guilty when she states, or it is apparent, that such argument is based solely on the evidence.” (People v. Cisewski (1987), 118 Ill. 2d 163, 178, citing People v. Tiller (1982), 94 Ill. 2d 303, 319.) We conclude that these remarks were based on the evidence and did not substantially prejudice defendant.
Defendant claims that the prosecutor improperly insinuated that defendant killed the victim because she resisted his attempt to rape her. During closing argument, a prosecutor stated:
*485“You heard [the] testimony of the medical examiner. She talked about some particular injuries which she called punctate wounds, five of them on the abdomen. *** Not quite piercing the skin, but leaving evidence of an injury; that was the defendant, and in his hand he held People’s Exhibit No. 1 and he was jabbing her and backing her deeper into the apartment, down this hallway, past the living room, towards the kitchen, towards the bedroom. And when he got level with the kitchen I believe [the victim] said no and at that time this man exploded into a homicidal frenzy; and you heard the evidence of the medical examiner of what he did to her: repeatedly stabbing and slashing her over and over again as she threw her arms up to defend herself. Didn’t deter him a bit. He stabbed her over and over again until she finally fell on the kitchen floor.”
During rebuttal, a prosecutor remarked as follows:
“Now, the People do have the burden of proof as to proving the defendant guilty beyond a reasonable doubt, but does that mean we have to prove all sorts of little side tangents beyond a reasonable doubt[?] The answer is no. The judge will give you a set of instructions. In other words, he will tell you what the law is in this case. All you have to do is take your good God-given common sense and mental abilities and ability to observe things and take those back to the jury room. One of the things that he will tell you is exactly what we have the burden of proof as to. Do we have the burden of proof as to the defendant’s motive? Do we have to show you beyond a reasonable doubt why he was going to attack [the victim]? The answer is no. We have the right to try to show you, if we wish, by inference, what his motives were; and you saw the photo of [the victim] and you saw how the lower part of her clothing was pulled up and how the bloodstains are on top of that clothing. Now, does that infer to you what his possible motives were in this case?”
We consider these remarks to be within the bounds of proper closing argument. We have recited at length the evidence adduced at trial; we need not repeat it here. After carefully reviewing the record, we conclude that the prose*486cutor’s remarks constituted a reasonable characterization of the evidence and logical inferences drawn therefrom. See People v. West (1990), 137 Ill. 2d 558, 592; People v. Collins (1985), 106 Ill. 2d 237, 277-78.
Defendant contends a prosecutor misstated the evidence on three occasions during rebuttal argument. The prosecutor remarked that defendant almost “got away” with destroying the evidentiary value of the knife; that the entire front portion of the knife had charred blood on it; and that the white powdery substance near the victim’s apartment door was sugar.
Additionally, defendant contends that during rebuttal argument, the prosecutor misstated the law. The prosecutor commented on the elements of the offense of home invasion.
Citing several of the prosecutor’s remarks, defendant argues that the prosecutor repeatedly and improperly expressed his personal opinion on the credibility of the witnesses, the victim’s character, and defendant’s motive. Defendant also argues that the prosecutor commented on the victim’s rights and the extent of the victim’s injuries with the intent of inflaming the passion and prejudice of the jury.
However, the record shows that for each of the above-stated alleged errors, defendant either failed to object at trial, or failed to include the specific alleged error in his post-trial motion, or both. Thus, these issues are waived. Enoch, 122 Ill. 2d at 186; People v. Phillips (1989), 186 Ill. App. 3d 668, 682; People v. Sargent (1989), 184 Ill. App. 3d 1016, 1024-25.
Sufficiency of the Evidence: Home Invasion
Defendant contends the State failed to prove beyond a reasonable doubt an element of the offense of home invasion. Of course, the State carries the burden of proving beyond a reasonable doubt each element of the offense and *487the defendant’s guilt. People v. Ware (1961), 23 Ill. 2d 59, 62.
It is the function of the jury to assess the credibility of the witnesses, the weight to be given their testimony, and the inferences to be drawn from the evidence. (People v. Brisbon (1985), 106 Ill. 2d 342, 360; People v. Zuniga (1973), 53 Ill. 2d 550, 559.) On appeal, a reviewing court, considering all of the evidence in the light most favorable to the prosecution, must determine whether any rational fact finder could have found beyond a reasonable doubt the essential elements of the crime. A criminal conviction will not be set aside unless the evidence is so improbable or unsatisfactory as to create a reasonable doubt of the defendant’s guilt. People v. Boclair (1989), 129 Ill. 2d 458, 474; Collins, 106 Ill. 2d at 261.
A person who is not a peace officer acting in the line of duty commits home invasion “when without authority he or she knowingly enters the dwelling place of another when he or she knows or has reason to know that one or more persons is present,” and he or she either (1) uses or threatens the imminent use of force with a dangerous weapon, or (2) intentionally causes injury, with which defendant was charged. (Ill. Rev. Stat. 1987, ch. 38, par. 12—11(a).) The gravamen of the offense is unauthorized entry. (People v. Campbell (1990), 199 Ill. App. 3d 775, 786.) Defendant contends the State failed to present any evidence that he entered the victim’s apartment without authority.
However, it is established that when a defendant comes to a private residence and is invited in by the occupant, the authorization to enter is limited. Criminal actions exceed this limited authority. (People v. Hudson (1983), 113 Ill. App. 3d 1041, 1044-45.) Thus, “consent given for a defendant’s entry is vitiated by criminal actions engaged in by the defendant after entering, thus making his entry *488unauthorized.” People v. Sanders (1991), 212 Ill. App. 3d 773, 778 (and cases cited therein).
After reviewing the evidence in the light most favorable to the prosecution, we conclude that the evidence established beyond a reasonable doubt the element of unauthorized entry. The evidence supports the inference that defendant gained access to the victim’s apartment through trickery and deceit, under the pretense of borrowing a cup of sugar. The evidence would permit a rational fact finder to conclude beyond a reasonable doubt that, regardless of how defendant entered the victim’s apartment, he exceeded his limited authority by stabbing the victim. (See, e.g., Sanders, 212 Ill. App. 3d at 778; Campbell, 199 Ill. App. 3d at 787; People v. Bruce (1989), 185 Ill. App. 3d 356, 373; People v. Davis (1988), 173 Ill. App. 3d 300, 305.) Further, we cannot say that the evidence is so improbable or unsatisfactory as to create a reasonable doubt of defendant’s guilt.
Concerning the sentencing hearing, defendant contends that he was denied a fair sentencing hearing because the trial judge: (1) failed to hold a hearing on the issue of proportionality; (2) denied defendant’s motion for a continuance for a neurological examination; (3) failed to hold a hearing to determine the voluntariness of defendant’s confession to a prior crime, and restricted cross-examination by the defense on the circumstances surrounding the confession; and (4) admitted into evidence unfounded testimony regarding a prior conviction. Defendant contends he was denied a fair sentencing hearing also because the prosecutor: (5) unfairly cross-examined a defense witness; and (6) made improper and prejudicial remarks during closing argument.
Defendant contends he was denied a fair sentencing hearing because the trial judge failed to hold a hearing on whether the death penalty is imposed in this State in an arbitrary or disproportionate manner. However, it is settled that the review of capital cases for proportionality is not required. Kubat, 94 Ill. 2d at 502-03, relying on People v. Brownell (1980), 79 Ill. 2d 508, 541-44.
Continuance for Neurological Examination
Defendant next contends he was denied a fair sentencing hearing because the trial judge denied his motion for a continuance for a neurological examination. At the sentencing hearing on April 6, 1990, defense counsel requested a continuance so that defendant could receive a neurological examination. Defense counsel stated that defendant suffered from spinal meningitis as a child and was injured in an automobile accident where he lost consciousness. Defense counsel further stated that an investigator from his office spoke with a psychologist, who opined that those two events may have caused defendant to have a neurological condition.
The trial judge denied the motion. Defendant asks this court to vacate his sentence and remand the cause for a new sentencing hearing.
The granting or denial of a continuance is a matter resting within the sound discretion of the trial judge, and a reviewing court will not interfere with his or her decision unless there has been a clear abuse of discretion. (Collins, 106 Ill. 2d at 281.) A trial judge does not abuse his or her discretion in denying a request for a mental examination where there is no indication that evidence of mitigating factors or rehabilitative potential might be present. People v. Stewart (1984), 101 Ill. 2d 470, 489-90.
*490In the present case, defendant’s neurological condition was not at issue during the trial. Defense counsel raised the possibility of a neurological condition for the first time at the sentencing hearing. Further, during the sentencing hearing, none of defendant’s witnesses in mitigation put his neurological condition at issue.
Also, the request for the neurological examination was not based upon expert testimony or similar evidence. Rather, the request was based on representations of what a psychologist opined. Further, nothing was presented to establish what the psychologist was told or the basis of the psychologist’s opinion. Nothing was presented to explain how the spinal meningitis or the automobile accident might have caused defendant to have a neurological condition.
Additionally, as the trial judge noted, the sentencing hearing did not conclude in one day. In fact, the next hearing date was April 12, 1990, six days after the denial of the continuance. Defendant thus had time to either receive the examination or gather sufficient information to indicate that evidence of mitigating factors or rehabilitative potential might be present. All of these facts distinguish this case from People v. Allen (1984), 101 Ill. 2d 24, 32-37, cited by defendant.
“A sentence will not be vacated on speculation of what a mental examination may have revealed, when a judge refused to order that examination, believing that the defendant failed to raise the issue of his mental condition.” (People v. Woods (1985), 134 Ill. App. 3d 294, 301, citing Stewart, 101 Ill. 2d at 490.) We cannot say that the trial judge abused his discretion in denying defendant’s request for a continuance for a neurological examination.
Confession to Prior Crime
During the aggravation portion of the sentencing hearing, the State presented a certified copy of defendant’s *4911983 conviction for attempted rape and residential burglary. Over defendant’s objection, the State also presented defendant’s custodial confession to those crimes through the testimony of Detective Pope. Defendant contends he was denied a fair sentencing hearing because the trial judge failed to hold a hearing to determine the voluntariness of his confession to those prior crimes, and restricted cross-examination by the defense on the circumstances surrounding the confession.
In Illinois, it is settled that “ ‘a constitutional right, like any other right of an accused, may be waived, and a voluntary plea of guilty waives all errors or irregularities that are not jurisdictional.’ ” (Del Vecchio, 105 Ill. 2d at 433, quoting People v. Brown (1969), 41 Ill. 2d 503, 505.) Issues waived by a defendant’s plea of guilty include the admissibility of his or her confession. People v. Stice (1987), 160 Ill. App. 3d 132, 138; People v. Good (1979), 68 Ill. App. 3d 333, 338.
Defendant claims that his guilty plea in the prior prosecution waived any challenge to the voluntariness of his confession only insofar as it affected that conviction. Citing Christenson v. State (1991), 261 Ga. 80, 91, 402 S.E.2d 41, 51, defendant argues that his confession to the prior crimes did not mean “that he waived objection to the use of an inadmissible statement at the sentencing phase of a subsequent, unrelated death penalty trial.”
We disagree. The facts in Del Vecchio, pertinent to this issue, are the same as those in the present case. In Del Vecchio, we rejected this exact argument and applied the above-stated general rule. Defendant fails to distinguish this issue from that decided in Del Vecchio. We find no error here. See Del Vecchio, 105 Ill. 2d at 433.
Defendant also contends the trial judge prejudicially restricted the scope of his cross-examination of Detective Pope. The trial judge prevented defendant from introducing Pope’s testimony at a preliminary hearing in the 1983 *492prosecution. Defendant claims that the trial judge precluded him from cross-examining Pope regarding the circumstances surrounding the taking of the confession.
It is settled that “[i]f a court rules that a confession is voluntary and admits it into evidence, the defendant still has a right to present evidence to the jury which affects the credibility and weight to be given the confession.” (People v. Fleming (1981), 103 Ill. App. 3d 194, 197, citing People v. Cook (1965), 33 Ill. 2d 363, 369-70; accord Crane v. Kentucky (1986), 476 U.S. 683, 90 L. Ed. 2d 636, 106 S. Ct. 2142.) However, this right of defendant does not diminish the general rule that “ ‘the latitude to be allowed in cross-examination of witnesses rests largely in the discretion of the trial court. Such cross-examination should be kept within fair and reasonable limits, and it is only in a case of clear abuse of such discretion, resulting in manifest prejudice to the defendant, that a reviewing court will interfere.’ ” People v. Gallo (1973), 54 Ill. 2d 343, 356 (and cases cited therein), quoting People v. Halteman (1956), 10 Ill. 2d 74, 86; see Crane, 476 U.S. at 689-90, 90 L. Ed. 2d at 644-45, 106 S. Ct. at 2146.
In the present case, we conclude that defendant was not precluded from cross-examining Detective Pope regarding defendant’s confession. The trial judge permitted Detective Pope to testify on direct examination with respect to the document containing defendant’s confession. However, defendant, during cross-examination, attempted to introduce Pope’s prior testimony at the preliminary hearing in the 1983 prosecution. In the exercise of sound discretion, the trial judge refused this information. The judge’s ruling fairly and reasonably limited Detective Pope’s cross-examination in relation to his direct examination.
To establish the circumstances surrounding the taking of the confession, defendant could have called other witnesses, cross-examined Detective Pope, or testified him*493self. But he chose not to follow any of these paths. These, facts distinguish this case from Crane, where the defendant was denied any attempt to introduce evidence of the circumstances of the taking of a confession. (Crane, 476 U.S. at 685-86, 90 L. Ed. 2d at 642, 106 S. Ct. at 2144.) We cannot say that the trial judge clearly abused his discretion, resulting in manifest prejudice to defendant.
Erroneously Admitted Evidence
Defendant claims that the trial judge denied him a fair sentencing hearing also by admitting into evidence unfounded testimony regarding a prior conviction. In People v. Jackson (1992), 149 Ill. 2d 540, this court recently repeated the following settled rule:
“While evidence of past criminal conduct is often not admissible at trial, it is relevant information at sentencing. Previous convictions are routinely considered. In addition, outstanding indictments or other criminal conduct for which there has been no prosecution or conviction may be considered in sentencing. Such evidence, however, should be presented by witnesses who can be confronted and cross-examined, rather than by hearsay allegations in the presentence report, and the defendant should have an opportunity to rebut the testimony.” Jackson, 149 Ill. 2d at 548.
See Brisbon, 106 Ill. 2d at 364-65.
During the aggravation portion of the sentencing hearing, the State presented the testimony of former Des Plaines Police Officer Carol Daugherty. Daugherty testified that on the afternoon of November 13, 1984, she was on patrol on a street in downtown Des Plaines. She observed a man chasing defendant down the street through rush-hour traffic. The man had blood on his back and a deep cut in the middle of the back. Defendant was holding in his hand a folding knife with a 31/2-inch long blade.
*494Following Daugherty’s testimony, the State established that defendant pled guilty to the reduced charge of battery. Also, at the time of the incident, defendant was on parole for his 1983 conviction. Based on a charge of aggravated battery and the parole violation of possessing a deadly weapon, i.e., the knife, defendant violated his parole. He was subsequently returned to prison.
Citing People v. Adams (1985), 109 Ill. 2d 102, 128-29, defendant argues that Daugherty’s testimony was inadmissible because it failed to establish that defendant was the aggressor or wrongdoer, or, if he was, that he had actually stabbed the man who had chased him.
However, defendant pled guilty to the reduced charge of battery. “When a plea of guilty is fairly and understandingly made, it admits every material fact alleged in the indictment and all the elements of the crime with which an accused is legally charged, and obviates the need of any proof whatsoever.” (People v. Wilfong (1960), 19 Ill. 2d 406, 409; People v. Baxton (1957), 10 Ill. 2d 295, 299.) Thus, by his guilty plea, defendant admitted that he was the wrongdoer and relieved the State from establishing that fact. We cannot say that the trial judge abused his discretion.
Prosecutor’s Unfair Cross-Examination
Defendant contends he was denied a fair sentencing hearing also because the prosecutor unfairly cross-examined defense witness Helen Shannon, defendant’s grandmother. During the mitigation portion of the sentencing hearing, Shannon testified that defendant had lived with her periodically until he was 14 years old. During that time, according to Shannon, defendant was a very obedient child, who did not have trouble either in school or in the neighborhood.
During cross-examination, a prosecutor asked Shannon whether she knew that defendant had been “kicked out of *495high school for being in trouble.” Shannon answered “No.” The State did not subsequently present evidence that defendant had been expelled from high school.
The record shows that defendant failed both to object to the question at trial and to include the issue in his post-trial motion; thus, the issue is waived. (Turner, 128 Ill. 2d at 555.) After reviewing the record, we further conclude that this issue does not warrant our consideration under the plain error doctrine. See Burns, 144 Ill. App. 3d at 358-59.
Prosecutor’s Improper Remarks
Defendant lastly contends he was denied a fair sentencing hearing because a prosecutor made the following improper and prejudicial remarks during closing argument:
“I’d like to talk a bit about his [defendant’s] testimony in this case. Judge, the defendant in this courtroom did not have to testify, but he chose to come up to the witness stand and raise his right hand and swear before [A]lmighty God to tell the truth, the whole truth, and nothing but the truth, and that means nothing to him. He denigrated the sanctity of this courtroom, a place where truth is supposed to be held sacred. He profaned this courtroom, a place where the truth is held sacred, when he looked those jurors in the eye and told them horrible lies about how the Schaumburg Police Department framed him and the reason he thought they did it was because they’re prejudiced out there in the northwest suburbs. After raising his right hand in a courtroom and swearing to tell the truth, he did that. He has no respect for the law.
I’d like the Court to take into consideration his demonstrated complete lack of remorse in word or deed. *** He’s cold and thinks only of himself. If the defendant at some point in these proceedings had admitted his guilt or had evidenced some type of remorse, that might have been considered a mitigating factor in your Honor’s eyes, *** but there has been nothing of the sort, ever.”
*496Defendant concedes that he failed to object at trial to these remarks. Therefore, the issue is waived. Enoch, 122 Ill. 2d at 186.
Sentencing Order Correction
We now address, sua sponte, an error in the sentencing order. The sentencing order states that defendant was convicted of one count of armed violence and sentenced on that conviction to a concurrent prison term of 30 years. However, according to the report of proceedings, the trial judge found that the armed violence conviction merged into the first degree murder conviction.
Where the sentence indicated in the common law record conflicts with the sentence imposed by the trial judge as indicated in the report of proceedings, the report of proceedings will prevail and the common law record must be corrected. (People v. Casiano (1991), 212 Ill. App. 3d 680, 690; People v. Thompson (1977), 51 Ill. App. 3d 447, 450.) Accordingly, we correct the sentencing order here, so that it reflects that defendant was convicted of one count of first degree murder, on which he was sentenced to death; and one count of aggravated arson and one count of home invasion, on which he was sentenced to two concurrent prison terms of 30 years. 134 Ill. 2d R. 615(b); see Thompson, 51 Ill. App. 3d at 450-51.
Constitutionality of the Illinois Death Penalty
Concerning the constitutionality of the Illinois death penalty statute, defendant contends the statute violates the United States and Illinois Constitutions because it: (1) vests unfettered discretion in a prosecutor to request a death penalty hearing; (2) places the risk of nonpersuasion at the sentencing hearing on the defendant; (3) does not require proportionality review; and (4) does not require the *497sentencing authority to determine whether death is an appropriate sentence.
However, the four arguments that defendant makes have been rejected by this court. We have held that the death penalty statute is not invalid for affording the prosecutor discretion in determining whether to seek the death penalty in a particular case. (People v. Maxwell (1992), 148 Ill. 2d 116, 149-50; Williams, 147 Ill. 2d at 264-66.) The death penalty statute is not invalid because, after a defendant is found eligible for a death sentence, the statute places the burden on the defendant to prove that a death sentence should not be imposed. (Williams, 147 Ill. 2d at 268-69; People v. Gosier (1991), 145 Ill. 2d 127, 163.) The death penalty statute is not invalid because it fails to provide for proportionality review. (Maxwell, 148 Ill. 2d at 150; Kubat, 94 Ill. 2d at 502-03.) Lastly, the death penalty statute is not invalid because it does not require the sentencing authority to make a separate, additional finding that death is the appropriate penalty in this case. (Maxwell, 148 Ill. 2d at 149; People v. Whitehead (1987), 116 Ill. 2d 425, 462-63.) Defendant fails to persuade us to reconsider this court’s prior holdings.
For the foregoing reasons, the judgment of the circuit court of Cook County is affirmed, and the common law record is corrected as stated in this opinion. The clerk of this court is directed to enter an order setting Tuesday, September 14, 1993, as the date on which the sentence of death, entered in the circuit court, is to be imposed. The defendant shall be executed in the manner provided by law. (Ill. Rev. Stat. 1991, ch. 38, par. 119 — 5.) The clerk of this court shall send a certified copy of the mandate in this case to the Director of Corrections, the warden of State-ville Correctional Center, and the warden of the institution where defendant is now confined.