Maciej Wazny appeals his convictions and 240-month total sentence for conspiracy to import Gamma-Butyrolactone (“GBL”) for human consumption into the United States from outside of the United States, in violation of 21 U.S.C. §§ 963 and 960(b)(3); of importation of GBL for human consumption into the United States from a place outside of the United States, in violation of 21 U.S.C. §§ 952, 802(32), 813 and 960(b)(3); and possession and distribution of GBL, for human consumption, after unlawfully importing the substance into the United States from a place outside the United States, in violation of 21 U.S.C. §§ 959, 802(34)(X), 813, 802(32) and 960(b)(3).1 On appeal, Wazny argues that: (1) the district court erred in admitting hearsay evidence under the statements of a co-conspirator exception; (2) his convictions were not supported by sufficient evidence; (3) the district court abused its discretion in giving a deliberate ignorance instruction; (4) and his sentence was procedurally and substantively unreasonable. After careful review, we affirm.
We review a district court’s evidentiary rulings for abuse of discretion. United States v. Massey, 89 F.3d 1433, 1441 (11th Cir.1996). We review a challenge to the sufficiency of the evidence de novo, viewing the evidence in the light most favorable to the government. United States v. Jones, 601 F.3d 1247, 1267 (11th Cir.2010). While we review the legal correctness of a jury instruction actually given de novo, jury instructions are subject to harmless error review. United States v. Webb, 655 F.3d 1238, 1249-50 n. 8 (11th Cir.2011); Fed.R.Civ.P. 61. An error is harmless unless “there is a reasonable likelihood that [it] affected the defendant’s substantial rights.” United States v. Hawkins, 905 F.2d 1489, 1493 (11th Cir.1990). We review the district court’s application and legal interpretations of the Guidelines de novo, and the district court’s factual determinations for clear error. United States v. Zaldivar, 615 F.3d 1346, 1350 (11th Cir.2010), cert. denied, — U.S. -, 131 S.Ct. 959, 178 L.Ed.2d 791 (2011). Lastly, we review the sentence a district court imposes for “reasonableness,” which “merely asks whether the trial court abused its discretion.” United States v. Pugh, 515 F.3d 1179, 1189 (11th Cir.2008) (quoting Rita v. United States, 551 U.S. 338, 351, 127 S.Ct. 2456, 168 L.Ed.2d 203 (2007)).
*50First, we are unpersuaded by Wazny’s claim that the district court erred in admitting hearsay evidence. All relevant evidence is presumed to be admissible. See Fed.R.Evid. 402. While evidence may constitute hearsay — an out-of-court statement introduced to prove the truth of the matter asserted — certain exceptions to the hearsay rule exist. See Fed.R.Evid. 801, 802. Moreover, evidence which is not hearsay need not fit into any exception to the rule excluding hearsay. See Untied States v. Mateos, 623 F.3d 1350, 1364 (11th Cir.2010), cert. denied, — U.S. -, 131 S.Ct. 1540, 179 L.Ed.2d 310 (2011). One exception to the hearsay rule applies to statements of a co-conspirator. In order to introduce these statements under Fed. R.Evid. 801(d)(2)(E), the government must prove by a preponderance of the evidence that (1) a conspiracy existed, (2) the conspiracy included the declarant and the defendant against whom the statement is offered, and (3) the statement was made during the course of and in furtherance of the conspiracy. United States v. Underwood, 446 F.3d 1340, 1345-46 (11th Cir.2006).
The Federal Rules of Evidence provide that evidence is properly authenticated when there is “evidence sufficient to support a finding that the matter in question is what its proponent claims.” Fed. R.Evid. 901(a). Authentication under Rule 901 only requires the presentation of “sufficient evidence to make out a prima facie case that the proffered evidence is what it purports to be. Once that prima facie showing has been made, the evidence should be admitted” and the trier of fact permitted to determine whether the proffered evidence is what it purports to be. United States v. Caldwell, 776 F.2d 989, 1001-02 (11th Cir.1985). The district court’s determination of authenticity should not be disturbed unless there is no competent evidence in the record to support it. United States v. Munoz, 16 F.3d 1116, 1120-21 (11th Cir.1994).
The Confrontation Clause bars the admission of “testimonial” hearsay unless the declarant is unavailable and the defendant had a prior opportunity for cross-examination. Crawford v. Washington, 541 U.S. 36, 68, 124 S.Ct. 1354, 158 L.Ed.2d 177 (2004). Hearsay statements are testimonial when, among other things, they are “made under circumstances which would lead an objective witness reasonably to believe that the statement would be available for use at a later trial.” Id. at 52, 124 S.Ct. 1354 (quotation omitted). Statements made in private conversation are generally nontestimonial because there is no reason to believe that the statements will be used at trial. See United States v. U.S. Infrastructure, Inc., 576 F.3d 1195, 1209 (11th Cir.2009).
Here, the district court did not err in admitting hearsay evidence under the co-conspirator’s statements exception. As for the undated video and the statements contained therein, a co-conspirator’s t-shirt and the apparent container of GBL were enough to establish that the video was made during the course of and in furtherance of the charged conspiracy. This conclusion was further supported by the audible word “GBL” along with Wazny’s statement expressing concern about driving on it.
As for the letter written by co-conspirator Brian Lang to Wazny, the letter was properly authenticated by a customs investigator, who testified as to how the letter was intercepted by prison officials and given to the investigator. Additionally, the introduction of Lang’s letter did not violate Wazny’s Sixth Amendment rights. The letter was comparable to a private conversation and there is no evidence whatsoever that Lang believed it *51would later be available for use at trial when he wrote it. Therefore, the letter was not testimonial in nature and Wazny’s inability to cross-examine Lang did not violate his Sixth Amendment rights. Accordingly, the district court did not abuse its discretion in admitting this evidence.
Next, we find no merit in Wazny’s argument that the evidence was insufficient to support his convictions. In considering the sufficiency of the evidence, we must decide whether any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt. United States v. Hernandez, 433 F.3d 1328, 1335 (11th Cir.2005). “[A] statement by a defendant, if disbelieved by the jury, may be considered as substantive evidence of the defendant’s guilt.” United States v. Brown, 53 F.3d 312, 314 (11th Cir.1995).
“To sustain a conviction for conspiracy [under 21 U.S.C. § 963], the government must prove beyond a reasonable doubt that (1) an illegal agreement existed; (2) the defendant knew of it; and (3) the defendant, with knowledge, voluntarily joined it.” Hernandez, 433 F.3d at 1333. The required elements of a conspiracy can be established by inference from the actions of the conspirators or by circumstantial evidence. United States v. Gianni, 678 F.2d 956, 959 (11th Cir.1982). To sustain a conviction for possession and distribution of GBL for human consumption, the government must prove that the defendant sold the GBL with the intention that it be used for human consumption, or the knowledge that it was being purchased for human consumption. See 21 U.S.C. § 813.
Viewing the evidence in the light most favorable to the government, there was sufficient evidence presented at trial to support the jury’s conclusion that Waz-ny was guilty beyond a reasonable doubt. First, there is sufficient evidence to support the conspiracy conviction. Wazny himself testified that he ran his internet business Cleanstar Poland with the help of his brother, and undisputed evidence showed that his wife also assisted in the running of the business, which essentially started following dissolution of Cleanstar Germany, which had sold GBL as a purported glue remover. The evidence further showed that Wazny was involved in some way with Brian Lang and Cleanstar Germany, and either Wanzy or someone on the video asked about taking GBL while driving in the company of Brian Lang and two of Wazny’s cousins. Taken together, these things provided sufficient evidence for a rational trier of fact to find a conspiracy, since the fact that Wazny ran Cleans-tar Poland with his family would be enough to satisfy the definition of a conspiracy.
There was also sufficient evidence to support the jury’s conclusion that Waz-ny was selling his product for human consumption. Wazny himself admitted that he knew GBL could be used for human consumption, and the video established that he had personal knowledge of that fact. In addition, Wazny testified in his own defense, and the jury was entitled to use his testimony against him and conclude that he was lying and therefore guilty. Thus the evidence was sufficient to sustain his convictions on each of the substantive counts.
We are likewise unpersuaded by Wazny’s argument that the district court abused its discretion in giving a deliberate ignorance instruction. A deliberate ignorance instruction is warranted when the facts “support the inference that the defendant was aware of a high probability of the existence of the fact in question and purposely contrived to avoid learning all of the facts in order to have a defense in the event of a subsequent prosecution.” Unit*52ed States v. Rivera, 944 F.2d 1568, 1571 (11th Cir.1991) (quotation omitted). We have held that instructing the jury on deliberate ignorance is harmless error where the jury was also instructed and could have convicted on an alternative, sufficiently supported theory of actual knowledge. United States v. Kennard, 472 F.3d 851, 858 (11th Cir.2006).
On this record, the district court did not abuse its discretion by instructing the jury on deliberate ignorance. For starters, there was evidence that Wazny had actual knowledge that his product was being used for human consumption. Conversely, because he denied any intent to sell GBL for personal consumption, a jury could have concluded that he was avoiding the knowledge that his product was being used for human consumption. But even assuming arguendo that the evidence was insufficient to show purposeful avoidance, any error by the district court was harmless, since there was sufficient evidence in this case to support a finding that Wazny had actual knowledge that his product was being used for human consumption.
Finally, we reject Wazny’s argument that his sentence was procedurally and substantively unreasonable. In reviewing sentences for reasonableness, we perform two steps. Pugh, 515 F.3d at 1190. First, we “ ‘ensure that the district court committed no significant procedural error, such as failing to calculate (or improperly calculating) the Guidelines range, treating the Guidelines as mandatory, failing to consider the § 3553(a) factors, selecting a sen-fence based on clearly erroneous facts, or failing to adequately explain the chosen sentence — including an explanation for any deviation from the Guidelines range.’ ” Id. (quoting Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007)).2
“[Fjactual findings used to support a sentencing enhancement must be based on reliable and specific evidence and cannot be based on speculation.” United States v. Newman, 614 F.3d 1232, 1238 (11th Cir.2010). The government bears the burden of proving the applicability of a Guidelines enhancement, while the defendant bears the burden of proving the applicability of a Guidelines reduction. United States v. Belfast, 611 F.3d 783, 823 (11th Cir.2010), cert. denied, — U.S. -, 131 S.Ct. 1511, 179 L.Ed.2d 334 (2011); Zaldivar, 615 F.3d at 1352.
Under U.S.S.G. § 2D1.1, the base offense level for a drug offense is generally calculated by determining the quantity of drugs attributable to a defendant. In cases “[wjhere there is no drug seizure or the amount seized does not reflect the scale of the offense, the court shall approximate the quantity of the controlled substance.” United States v. Frazier, 89 F.3d 1501, 1506 (11th Cir.1996) (quotation omitted). The court may base its approximation on evidence of the average frequency and amount of the defendant’s drug sales. Id. Nevertheless, the court’s approximation of the drug amount must be “fair, accurate, and conservative,” and not “merely speculative.” United States v. *53Zapata, 139 F.3d 1355, 1359 (11th Cir.1998).
Under U.S.S.G. § 3C1.1, the district court may increase the defendant’s guideline range by two levels if “(A) the defendant willfully obstructed or impeded, or attempted to obstruct or impede, the administration of justice with respect to the investigation, prosecution, or sentencing of the instant offense of conviction, and (B) the obstructive conduct related to (i) the defendant’s offense of conviction and any relevant conduct; or (ii) a closely related offense.” A “sentencing judge clearly has the authority to enhance a defendant’s offense level if the judge makes an independent factual finding that the defendant willfully lied in trial testimony.” United States v. Husky, 924 F.2d 223, 224 (11th Cir.1991).
If we conclude that the district court did not procedurally err, we must consider the “ ‘substantive reasonableness of the sentence imposed under an abuse-of-diseretion standard,’ ” based on the “ ‘totality of the circumstances.’ ” Pugh, 515 F.3d at 1190 (quoting Gall, 552 U.S. at 51, 128 S.Ct. 586). This review is “deferential,” requiring us to determine “whether the sentence imposed by the district court fails to achieve the purposes of sentencing as stated in section 3553(a).” United States v. Talley, 431 F.3d 784, 788 (11th Cir.2005). We will “vacate the sentence if, but only if, we are left with the definite and firm conviction that the district court committed a clear error of judgment in weighing the § 3553(a) factors by arriving at a sentence that lies outside the range of reasonable sentences dictated by the facts of the case.” United States v. Irey, 612 F.3d 1160, 1190 (11th Cir.2010) (en banc) (quotation omitted), cert. denied, — U.S. -, 131 S.Ct. 1813, 179 L.Ed.2d 772 (2011). “The party challenging the sentence bears the burden to show it is unreasonable in light of the record and the § 3553(a) factors.” United States v. Tome, 611 F.3d 1371, 1378 (11th Cir.2010), cert. denied, — U.S. -, 131 S.Ct. 674, 178 L.Ed.2d 502 (2010).
Wazny has not shown that his sentence was procedurally unreasonable. For starters, the district court did not clearly err in calculating the amounts of GBL attributed to Wazny since this amount was undisputed, and derived from Wazny’s testimony and business records, which showed that he purchased 4600 kilograms of GBL from his supplier during the time period that he operated Cleanstar Poland. There was also no error in calculating this amount since, as noted above, the government presented sufficient evidence at trial to show that Wazny knew the product was being used for human consumption. Nor did the district court clearly err in applying the obstruction of justice enhancement. The district court’s finding that Wazny willfully lied at trial, in conjunction with the jury’s verdict of guilty, was enough for the district court to properly apply an obstruction of justice enhancement.
Wazny’s sentence was also substantively reasonable. Wazny’s sentence, at the statutory maximum, was still 120 months below the guideline range. And while Waz-ny’s total sentence was higher than his co-conspirator’s, Wazny was also held accountable for a much larger quantity of GBL. Moreover, the record shows that the district court clearly considered all of the § 3553(a) factors when it imposed the sentence. Accordingly, his sentence was reasonable, and we affirm.
AFFIRMED.