Appellant, Sandra Colleen Roberts, appeals the order of the Washington County Circuit Court finding her guilty of driving without a license, of violating Arkansas Code Annotated § 5-65-303 (Repl. 1993) of the “Underage Driving Under the Influence Law” codified at Arkansas Code Annotated §§ 5-65-301 to -311 (Repl. 1993 & Supp. 1995) (“Underage DUI Law”), and of direct contempt of court. Appellant raises four arguments for reversal. Jurisdiction is properly in this court pursuant to Ark. Sup. Ct. R. l-2(a)(l) and (3). We affirm the trial court’s judgment as modified.
The parties stipulated below to the following facts. On September 25, 1993, appellant was arrested at a roadblock for driving under the influence and having no driver’s license. At that time, appellant was aged sixteen years, unemployed, and a high-school student. Approximately fifty-six minutes after the traffic stop, appellant registered 0.05% blood alcohol after taking a certified BAC DataMaster test. Appellant does not contest the legality of the traffic stop or the results of the blood-alcohol test.
1. Public-service work
Appellant’s first argument assails the constitutionality of section 5-65-306, the public-service work provision of the Underage DUI Law. Section 5-65-306 provides as follows:
*71Any underage person who pleads guilty or nolo con-tendere or is found guilty of violating § 5-65-303 shall be ordered by the court to perform public service work of the type and for the duration as deemed appropriate by the court.
Appellant summarily argues, without citation to authority, that section 5-65-306 violates our state constitutional due-process guarantee, Ark. Const, art. 2, § 8, because it authorizes a trial court to pronounce a penalty of indefinite duration, and violates our state constitutional equal-protection guarantee, Ark. Const, art. 2, § 18, because it applies only to underage persons. The trial court sentenced appellant to perform thirty hours of public service for the substance-abuse program of the Salvation Army in Fayetteville.
We do not reach the merits of this argument. We do not consider an argument, even a constitutional one, when the appellant presents no citation to authority or convincing argument in its support and it is not apparent without further research that the argument is well taken. E.g., Cook v. State, 321 Ark. 641, 906 S.W.2d 681 (1995); Stevens v. State, 319 Ark. 640, 893 S.W.2d 773 (1995). This rule is consistent with the well-established principle that statutes are presumed to be constitutional and the burden of proving otherwise rests with the party challenging the statute. E.g., Dougan v. State, 322 Ark. 384, 912 S.W.2d 400 (1995); Cook, 321 Ark. 641, 906 S.W.2d 681. Appellant does not explain how the General Assembly’s failure to express a statutory maximum duration for community service pursuant to section 5-65-306 offends her due-process right, or how the statute’s underage classification offends her equal-protection right. We do not consider such deficient contentions on appeal. Cook, 321 Ark. 641, 906 S.W.2d 681; Stevens, 319 Ark. 640, 893 S.W.2d 773.
2. Blood-alcohol test
Without reference to any statute, appellant’s second argument is that she refused a second blood-alcohol test due to indigence, and that the state should have paid for the additional test and later taxed its cost to her because it is a violation of Arkansas Constitution, Article 2, section 18, and the United States Constitution, Amendment 14, to allow “people of means to get a second test, but to deny that right to an indigent person[.]” We are aware that the implied-consent provision of the Underage DUI Law, section 5-*7265-309(a), provides that an underage driver shall be deemed to have consented, subject to the provisions of Arkansas Code Annotated § 5-65-203 (Repl. 1993), to a chemical test or tests of her blood, breath, or urine for the purpose of determining its alcohol or controlled-substance content. Section 5-65-203 (b)(1), in turn, provides that, if a person whose blood alcohol is tested by a law enforcement officer requests an additional test, the cost of the second test shall be borne by the person tested.
We do not reach the merits of this argument. First, the record does not establish that appellant refused an additional test because she lacked the funds to pay for it. As appellant’s counsel conceded in oral argument before this court, appellant did not tell anyone at the time of her arrest that she wanted an additional blood-alcohol test or that she could not afford to pay for one. Further, the record fails to establish that appellant was indigent at the time of her arrest. Appellant contends that she was at least “temporarily indigent” on the basis of the stipulated fact that she was an unemployed minor student at the time of the arrest. This contention is not persuasive. Indigent status is a mixed question of fact and law to be determined upon consideration of such factors as the individual’s total income, including income from unemployment benefits, total assets, total indebtedness, able-bodiedness, and level of education. Hill v. State, 305 Ark. 193, 805 S.W.2d 651 (1991). No finding of indigence was made by the trial court in this case, nor did the parties stipulate that appellant was indigent at the time of the arrest.
Second, appellant fails to establish that she was prejudiced by the absence of an additional test. Appellant stipulated that her blood alcohol registered 0.05% as a result of the test that was administered by the law enforcement officer after the traffic stop. The Underage DUI Law proscribes the operation or actual physical control of a motor vehicle by an underage person if, at that time, there was 0.02% but less than 0.10% by weight of alcohol in the person’s blood as determined by chemical test. Section 5-65-303(b). Below, appellant stipulated that she did not contest the legality of the 0.05% blood-alcohol test result or the traffic stop, and raised no argument demonstrating that a second test was necessary to an adequate defense.
Appellant also argues that the state’s failure to pay for an additional test violated her state and federal constitutional rights to *73gather exculpatory evidence. Ark. Const, art. 2, § 10; U.S. Const, amend. 6. This argument is without merit on the facts of this case in which, as we have noted, appellant stipulated to the accuracy of the 0.05% blood-alcohol test result and raised no argument demonstrating the necessity of a second test to an adequate defense. Appellant’s counsel contended in oral argument before this court, that had a higher second-test result been obtained, it would have shown that appellant’s blood-alcohol level was rising with the passage of time and therefore was less than 0.02% at the time she was operating her vehicle. The record, however, fails to reveal that this speculative contention was raised before the trial court, thus, we do not consider it for the first time on appeal. Parnell v. State, 323 Ark. 34, 912 S.W.2d 422 (1996).
Finally, appellant contends that due to the aforementioned alleged constitutional violations, her consent to take the test that was administered by the law enforcement officer was involuntarily given. This argument, which is based upon a false premise, is without merit. Sasser v. State, 321 Ark. 438, 902 S.W.2d 773 (1995).
3. Contempt
Appellant’s third argument is that the trial court erred in finding her in contempt of court for her refusal to attend a presentencing screening at Ozark Guidance Center. Appellant argues that the contempt ruling was erroneous because her participation in the screening would violate her constitutional right against self-incrimination and because she did not waive her right to a jury trial on the contempt charge. We have recently considered and rejected both of these arguments in Watson v. City of Fayetteville, 322 Ark. 324, 909 S.W.2d 637 (1995), which controls this case.
4. Jail sentence
The trial court sentenced appellant to a suspended sentence of thirty days in jail, with credit for one day served. Appellant’s fourth argument is that a jail sentence for violating section 5-65-303 is illegal on its face because the trial court lacked authority to impose it. See sections 5-65-304 (suspension of driver’s license), -305 (monetary fine), -306 (public-service work), -307 (alcohol and driving-education program), and -311 (relationship to other laws). Although appellant did not raise this issue below, she is not precluded from raising it on appeal because we treat an allegation of an illegal sentence as a problem of subject-matter jurisdiction that *74we may review whether or not an objection was made in the trial court. Bilderback v. State, 319 Ark. 643, 893 S.W.2d 780 (1995); Howard v. State, 289 Ark. 587, 715 S.W.2d 440 (1986).
The state concedes the jail sentence was not authorized by statute and we agree. The jail sentence is illegal on its face because the trial court lacked authority to impose it. Richards v. State, 309 Ark. 133, 827 S.W.2d 155 (1992). Where the trial court’s error has nothing to do with the issue of culpability and relates only to punishment, we may correct the error in lieu of reversing and remanding the case. Bangs v. State, 310 Ark. 235, 835 S.W.2d 294 (1992); Richards, 309 Ark. 133, 827 S.W.2d 155. Thus we modify appellant’s sentence for violating section 5-65-303 by deleting the suspended sentence of thirty days in jail with credit for one day served.
The trial court’s judgment of conviction and sentence is affirmed as modified.