The defendant, Steve Safa,1 was found guilty by a jury on one count of making a false declaration before a grand jury and was sentenced to serve 15 months in prison and pay a fine of $10,000. On appeal, the defendant contends that the district court admitted into evidence improper lay opinion testimony and failed to consider the necessary factors in imposing sentence. For the reasons set out below, we find no reversible error and affirm the judgment of the district court in its entirety.
FACTUAL AND PROCEDURAL BACKGROUND
The events giving rise to this prosecution began in September 2001, when Chief Deputy Sheriff Ronald Jones stopped a sport utility vehicle pulling a U-Haul trailer that was drifting from one lane of traffic to the other on northbound 1-71 in Oldham County, Kentucky. Investigation revealed that the vehicle was en route to Detroit, Michigan. Its driver, Mohamad El-Ha-rake, later gave Jones consent to search the trailer, in which the law enforcement officer found chewing tobacco, pipe tobacco, and 1,500 cartons of Marlboro cigarettes, some with Kentucky tax stamps affixed to them, others with no tax stamps at all. According to Deputy Jones, the passenger in the vehicle, Steve Safa, admitted knowing there were cigarettes in the trailer, although Safa later testified at trial that he never made such an admission to the deputy.
Because El-Harake and Safa appeared to be engaged in the illegal transportation of contraband cigarettes, Jones detained both men and eventually involved federal agents and agencies in the investigation. *820Subsequently, Safa was summoned before a federal grand jury looking into a possible conspiracy between El-Harake and other individuals that involved cigarette-trafficking and other federal crimes. While the defendant was under oath before the grand jury, Assistant United States Attorney Robert Cares asked him a number of questions, including the following:
Do you have any reason to believe that there were cigarettes in that U-Haul van?
Do you know Ali Farhat?
Have you ever talked with Ali Farhat?
Do you know somebody by the name of Fadi or Fadi Haydous? Let me spell that. F-a-d-i H-a-y-d-o-u-s.
Safa responded “no” or “no, sir” to each inquiry. Alleging those answers to be false, however, the government obtained a three-count indictment against the defendant charging three instances of false statements before the grand jury in violation of 18 U.S.C. § 1623.
At trial, the government offered testimony that Safa actually helped load the contraband cigarettes into the U-Haul trailer rented by El-Harake; that the defendant and Ali Farhat seemed to know each other; and that the defendant knew Fadi Haydous, bought contraband cigarettes from Haydous, and received large money transfers totaling at least $44,000 from Haydous. Assistant United States Attorney Cares also testified, over defense counsel’s objection, that truthful answers from Safa during the grand jury proceedings to inquiries concerning the defendant’s knowledge of cigarettes in the U-Haul trailer and Safa’s acquaintance with Ali Farhat and Fadi Haydous “would ... have assisted the Grand Jury’s investigation” and that false answers “had a natural tendency to influence, impede, or dissuade the Grand Jury’s investigation.”
Taking the stand in his own defense, Safa testified that he knew that El-Harake was transporting cigars and chewing tobacco on the date that they were stopped in Kentucky, but that he was not aware that contraband cigarettes were also in the trailer. Furthermore, Safa denied knowing Ali Farhat or Fadi Haydous, having any business dealings with Haydous, or being involved in any money transfers with Haydous. The jury obviously credited some of the defendant’s testimony because the jurors acquitted Safa of the first two counts of making a false declaration before the grand jury and convicted him only of falsely denying that he knew Fadi Hay-dous, a statement that was material to the government’s investigation of wide-ranging conspiracy charges.
After a hearing, the district judge sentenced Safa to 15 months in prison and fined him $10,000. From that judgment, the defendant now appeals.
DISCUSSION
In his first issue on appeal, Safa challenges the decision of the district judge to admit testimony from Assistant United States Attorney Cares regarding the effect that statements given by the defendant before the grand jury had on the government’s investigation into an ongoing conspiracy. According to the defendant, such testimony amounted to an improper lay opinion involving a legal conclusion, specifically whether Safa’s grand jury testimony was “material.”
A district court’s ruling on the admissibility of testimony is reviewed by this court only for an abuse of discretion. See Trepel v. Roadway Express, Inc., 194 F.3d 708, 716 (6th Cir.1999) (citing Gen. Elec. Co. v. Joiner, 522 U.S. 136, 141, 118 S.Ct. 512, 139 L.Ed.2d 508 (1997)). “An abuse of discretion exists when the district court applies the wrong legal standard, misap*821plies the correct legal standard, or relies on clearly erroneous findings of fact.” First Tech. Safety Sys., Inc. v. Depinet, 11 F.3d 641, 647 (6th Cir.1993).
To convict an individual of a violation of 18 U.S.C. § 1623, the government must prove beyond a reasonable doubt that the defendant “(1) knowingly made; (2) a materially false declaration; (3) under oath; (4) in a proceeding before or ancillary to any court of the United States.” United States v. Lee, 359 F.3d 412, 419 (6th Cir.2004) (emphasis added). Thus, the materiality of the declaration is an element of the offense that must be found by the jury. See United States v. Gaudin, 515 U.S. 506, 511, 115 S.Ct. 2310, 132 L.Ed.2d 444 (1995). Safa submits, consequently, that prosecution witnesses may not offer their opinions as to whether certain statements made during grand jury proceedings were indeed “material” because such testimony conveys “the witnesses] unexpressed, and perhaps erroneous, legal standards to the jury.” Torres v. County of Oakland, 758 F.2d 147, 150 (6th Cir.1985).
The defendant is correct in contending that witness testimony would improperly invade the province of the court to explain the applicable law to the jury if a witness were permitted to define “materiality.” However, the district judge in this case properly sustained Safa’s objection to the question, “Now, can you briefly, sir, explain to the members of the jury what does it mean for a question to be material before the Grand Jury?” Nevertheless, Assistant United States Attorney Cares was allowed to testify to facts that the jurors could accept or reject in reaching their conclusion as to whether Safa’s statements were “material.”
Although Rule 704 of the Federal Rules of Evidence provides that “testimony in the form of an opinion or inference otherwise admissible is not objectionable because it embraces an ultimate issue to be decided by the trier of fact,” we have consistently recognized that “opinions phrased in terms of inadequately explored legal criteria” should be excluded from evidence. See Torres, 758 F.2d at 150 (quoting Advisory Committee Notes to Federal Rule of Evidence 704). As explained in those Notes:
Thus the question, “Did T have capacity to make a will?” would be excluded, while the question, “Did T have sufficient mental capacity to know the nature and extent of his property and the natural objects of his bounty and to formulate a rational scheme of distribution?” would be allowed.
Id. Explained differently, “if the [witness] expresses an opinion using legal terms that follow the statutes ..., it is more likely to be held that the [witness] is giving a legal conclusion. In contrast, ... testimony that uses words that do not have specialized legal meaning is more likely to be admissible.” 4 Jack B. Weinstein & Margaret A. Berger, Weinstein’s Federal Evidence, § 704.04[1] (Joseph M. McLaughlin, ed., Matthew Bender 2d ed.2006) (citations and footnotes omitted).
In this case, the jury was charged with the responsibility to determine whether the alleged false statements made by Safa before the grand jury were so “material” as to affect the government’s investigation into a possible conspiracy to distribute contraband goods. In order to provide evidence upon which the jurors could base their conclusion with regard to such an inquiry, the prosecution was allowed to ask an Assistant United States Attorney whether Safa’s answers, “if false, would ... have influenced, impeded, or dissuaded the Grand Jury’s investigation” and, if true, “would ... have assisted the Grand Jury’s investigation.” Although those *822questions paraphrased the definition of “material” that the district judge later charged to the jury, they did not ask the witness to reach the very legal and factual conclusions for which the jury was responsible. Indeed, without the information provided by the witness in response to the challenged questions, the jurors would have had no information on which to base their verdict because they could not have intuitively ascertained the relevance of Safa’s testimony to the larger conspiracy investigation. The district judge, therefore, properly forbade the prosecution witness from explaining the concept of a “material question,” but he properly allowed that same witness to testify that Safa’s responses to inquiries before the grand jury did indeed have an impact upon the government’s investigatory strategies. We find no abuse of discretion in this regard.
In his second issue, Safa contends that the district judge imposed a procedurally unreasonable sentence upon him because the court failed to acknowledge its authority, other than under a sentencing guidelines scheme, to impose punishment that varied from the range of imprisonment envisioned by those now-advisory guidelines. According to the defendant, had the district judge taken into account the various factors listed in 18 U.S.C. § 3553(a), he would have imposed a sentence calling for probation, home detention, or some other alternative to incarceration for this first offense.
As has now been well-documented, the United States Supreme Court in United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), “invalidated the mandatory use of the Sentencing Guidelines and held they are now ‘effectively advisory.’” United States v. Collington, 461 F.3d 805, 807 (6th Cir.2006). Consequently, we now review any sentence imposed by a district judge to determine whether that sentence is “reasonable,” both procedurally and substantively. As we explained in Collington:
A sentence may be procedurally unreasonable if “the district judge fails to ‘consider’ the applicable Guidelines range or neglects to ‘consider’ the other factors listed in 18 U.S.C. § 3553(a), and instead simply selects what the judge deems an appropriate sentence without such required consideration.” A sentence may be considered substantively unreasonable when the district court “select[s] the sentence arbitrarily, bas[es] the sentence on impermissible factors, fail[s] to consider pertinent § 3553(a) factors or giv[es] an unreasonable amount of weight to any pertinent factor.”
Id. at 808 (citations omitted).
Unlike other cases that have found their way before us on appellate review, in this case the district judge did not allow a simple recitation of the § 3553(a) factors to substitute for a reasoned discussion and analysis of those considerations. Rather, Judge Tarnow took the time necessary to honor the spirit, as well as the letter, of our post -Booker decisions with an extended explanation, as follows:
Now, it’s my understanding that under Booker I start with that guideline range, which is 15 to 21 months. And that’s almost presumptively presumed, to be redundant, is presumed to be reasonable. I understand I have the discretion to find that it’s either too high or too low and I can depart in either direction. And having said that and having considered the fact that Mr. Safa is not a physical threat, and understanding the importance of family, but also understanding and agreeing with the Government that lying to a Grand Jury is a very serious offense and it is a threat to *823the entire system — and while the lying was not as serious as it could have been if the jury had convicted him of all three counts — and I certainly remember that the jury acquitted him of two counts. And those two counts are not being used to compute or to aggravate his sentence or to change his sentence upward — I’m still faced with a conviction on Count 3 of perjury, and the statute calls for a maximum of five years.
And I agree with you, Mr. Safa, I don’t think you will do this again. So, in terms of deterrence to you, just going through the process, facing the pressures of a trial and the negative publicity of being accused of lying to a Grand Jury, having to face your family and friends with that hanging over your head, are serious deterrents to you doing this again. However, there has to be some deterrence to other people.
And while I understand you have four small children and a family that needs your presence, I also understand that almost everyone who stands where you’re standing could say that. And it has already been taken into consideration in terms of the guidelines, but I’m also taking it into consideration as a basis of going below the guidelines.
I am not persuaded that your relationship to your family is much different than hopefully anyone’s relationship to their family. Your responsibilities to your family are very important, but not irreplaceable.
And the advantage perhaps of having some assets is that if any of them — and I’m looking at a financial statement that shows a net worth of approximately $6 million. If any of those assets are sella-ble, people can be hired to either run your businesses or to help with your family in terms of getting them to their doctor appointments and grocery shopping and the other things that are involved in being a husband and a father. Having taken into consideration the factors of 18 U.S.C. 3553(a) and the guidelines, pursuant to the Sentencing Reform Act of 1984, as to Count 3, it is the sentence of the Court that you, Mr. Safa, will serve a period of 15 months, which is the bottom of the guideline range, and you shall be placed on supervised release for a period of two years.
A fine is ordered in the amount of $10,000, payable immediately. There’s an assessment of $100, which is also payable immediately.
Without question, the district judge fully considered the factors listed in § 3553(a) before imposing sentence upon the defendant. Furthermore, he engaged in a reasoned analysis of how those factors related to other concerns expressed by Safa during the sentencing hearing. The district court thus clearly met the standards set for establishing procedural reasonableness.
When reviewing a sentence to determine whether it is substantively reasonable, we start with a presumption of reasonableness “[w]hen the district court issues a within-guidelines sentence.” United States v. Davis, 458 F.3d 491, 496 (6th Cir.2006), petition for cert. filed, (U.S. Nov. 13, 2006) (No. 06-7784). The presumptive reasonableness of the 15-month sentence in this case has not been rebutted by any evidence or argument advanced by Safa. Although the defendant requested imposition of a sentence that did not include incarceration, the district judge felt that a prison term was appropriate, even in a ease in which the likelihood that the defendant would commit additional crimes was extremely low, simply to emphasize to the public at-large the seriousness of lying under oath and the drastic consequences *824that will result from such disrespect for the judicial system as a whole.
The district judge in this matter recognized the advisory nature of the sentencing guidelines and his authority to impose any reasonable sentence justified by a consideration of the applicable statutory sentencing factors. We conclude that the court adequately justified the sentence imposed.
CONCLUSION
For the reasons set out above, we AFFIRM the judgment of the district court in its entirety.