AMENDED OPINION
JOHN M. WALKER, JR., Circuit Judge:Defendants-appellants Kalmen Stern (“Stern”), David Goldstein (“Goldstein”), Jacob Elbaum (“Elbaum”), and Benjamin Berger (“Berger”) appeal from the November 1999 judgments of conviction entered and sentences imposed by the district court upon jury verdicts of guilty. They raise a number of issues on appeal. First, and most importantly, the appellants allege that they were improperly convicted of the fraud conspiracy charged in the indictment because the evidence showed multiple conspiracies rather than a single conspiracy and this variance was substantially prejudicial. Second, Berger *111contends that his convictions should be reversed because the evidence was insufficient to sustain the conspiracy charge against him and there was a constructive amendment of the major substantive charge against him. Third, Goldstein argues that his convictions should be reversed because he withdrew from the conspiracy in 1991 and thus most of the charges against him were time-barred. Fourth, all four appellants claim that the district court erred in rejecting their claim under Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986), concerning the prosecutor’s use of a peremptory challenge to strike a Jewish prospective juror. Finally, they allege that the district court erred in enhancing their sentences under U.S.S.G. § 2Fl.l(b)(4)(A) for misrepresentation of affiliation with an educational institution.
We conclude that: (1) the appellants were properly convicted of the conspiracy as charged because the evidence was sufficient to support a jury finding of a single conspiracy rather than multiple conspiracies; (2) Berger’s convictions should be upheld since there was sufficient evidence of his knowing participation in the conspiracy and no constructive amendment of the charges against him; (3) Goldstein’s convictions should be upheld because he did not establish withdrawal as a matter of law; (4) the district court properly rejected the Batson claim; and (5) the court properly enhanced the appellants’ sentences for misrepresentation of affiliation with an educational institution. Accordingly, we affirm the judgment of the district court in all respects.
BACKGROUND
The original indictment charged the appellants and two other defendants (now fugitives), Chaim Berger and Avrum David Friesel, with conspiracy and substantive counts based upon their participation in a massive conspiracy to defraud the Department of Education (“DOE”), the Department of Housing and Urban Development (“HUD”), the Small Business Administration (“SBA”), the Social Security Administration (“SSA”), and the Internal Revenue Service (“IRS”). A redacted indictment, used at trial, eliminated charges against the fugitive defendants. Count 1 ■ of the redacted indictment charged all four appellants with conspiracy to defraud several federal agencies. The remaining counts charged the appellants, in various combinations, with substantive crimes relating,to this conspiracy, including embezzlement, mail fraud, wire fraud, false statements, money.laundering, filing a false tax return, and failing to file a tax return.
The ‘evidence at trial, taken in the light most favorable to the government following the jury verdict in its favor, revealed that the appellants — most of whom resided in New Square, a Hasidic Jewish community in Rockland County, New York — participated in a massive conspiracy to obtain by fraud millions of dollars in student financial aid, rental subsidies, social security benefits, and small ■ business loans. All four appellants' participated in.-a fraud upon the DOE, which formed the centerpiece of the government’s case, but the government also proved that the conspirators or subsets of them victimized other agencies as well. They' also concealed their income to increase the amounts they could obtain under federal subsidy programs and reduce their tax liability. The conspiracy involved a number of other participants, including major figures in the New Square Hasidic community. We now examine the scheme in greater detail.
First, the conspirators 'defrauded the DOE’s Pell Grant Program by falsely enrolling-thousands of New Square residents and others in schools offering mentor-based independent study programs. Many students never actually studied at these institutions, even though the conspirators prepared a paper record of their academic progress. Ultimately, most of the false students were enrolled at Toldos Yakov Yosef Seminary (“TYY”), an institution that purported to employ all four appel*112lants and received over $11 million in Pell Grants but never existed except on paper. As part of the conspiracy, the conspirators made extensive efforts to deceive the Accrediting Council for Continuing Education and Training (“ACCET”) in order to gain accreditation for TYY so that the school could qualify for federal aid.
Each of the appellants played a role in TYY. Elbaum was named as Board Secretary and had signature authority over bank accounts into which Pell Grant funds were wire-transferred and out of which payments were made to community organizations, to conspirators, and to the DOE (to repay student loans). Stern was named as Administrator (1987-88); pretended to be Arye Reich, the supposed Registrar — who was living in Israel at the time — during ACCET visits; and made false statements to the accreditors in this capacity. Goldstein was named as Administrator (1988-91) and helped deceive the accreditors in 1989. He resigned in 1991 and later served on the ACCET Board of Trustees. In addition, he made statements to a DOE investigator in 1996 that maintained the fiction of TYY, identifying officials and claiming to have fulfilled the duties of Administrator while at TYY. Finally, Berger served as an alleged mentor, and paychecks for supposed TYY employee Cheindel Bernat — Ayre Reich’s daughter, who also lived in Israel — were deposited into a bank account controlled by Berger in Bernat’s name.
Second, the conspirators defrauded HUD’s Section 8 housing subsidy program. Elbaum and Stern failed to report to HUD payments they received from accounts controlled by Chaim Berger, thus fraudulently increasing the amount of Section 8 subsidies for which they could qualify as tenants. Benjamin Berger fraudulently obtained Section 8 rent payments as a landlord by disguising his ownership of property in New Square — placing it in Cheindel Bernat’s name — and then depositing checks from HUD in an account he controlled in Bernat’s name. In addition, Berger obtained greater subsidies as a Section 8 tenant in Spring Valley by failing to report the income he received as a shadow landlord.
Third, various conspirators, including Goldstein and Stern, participated in schemes to defraud the SSA and the SBA, the details of which are not relevant to this appeal.
Fourth, the conspirators attempted to disguise from the IRS the income that they had diverted to the New Square community and to themselves through the above schemes. Elbaum and Stern received proceeds through off-the-books payments made from accounts controlled by Chaim Berger. Elbaum also failed to file a tax return for one year. Finally, Berger received and concealed income through his control of an account in Cheindel Bernat’s name.
The defendants moved to dismiss some or all of the counts against them on various grounds. The district court denied these motions. See United States v. Berger, 22 F.Supp.2d 145 (S.D.N.Y.1998); United States v. Stern, No. 97-CR-410(BSJ), 1998 WL 818477 (S.D.N.Y. Nov.19, 1998). On issues relevant to this appeal, the district court held that: (1) the conspiracy charge did not improperly combine multiple distinct crimes into a single count; (2) various charges against Gold-stein did not need to be dismissed as time-barred, since whether he successfully withdrew from the conspiracy in 1991 was an issue of fact for the jury to decide; and (3) the government’s intended proof on the wire fraud count against Berger did not vary impermissibly from the transaction alleged in the indictment.
On January 25, 1999, after a two-and-a-half month trial, the jury returned verdicts of guilty against all the appellants on all counts. In November 1999, the district court sentenced the appellants to prison terms ranging from 30 to 78 months and ordered them to pay restitution ranging *113from about $500,000 ■ to over $10 million. This appeal followed.
DISCUSSION
I. The Conspiracy Charge
The appellants contend that: (1) the jury was erroneously instructed on the conspiracy charge; (2) the evidence proved multiple conspiracies rather than the single conspiracy charged; and (3) the variance was prejudicial and requires reversal. We conclude that the appellants were properly convicted of the single conspiracy charged in the redacted indictment.
First,, the jury was properly instructed on the issue of single versus multiple conspiracies. In the basic charge, the district court fully covered the issue. When, during its deliberations, the jury requested a more detailed explanation of these issues, the court responded with the following supplemental instruction, which the appellants challenge here:
First, you should consider whether the conspiracy charged in Count 1 existed. In doing so, you must consider whether two or more conspirators agreed to accomplish at least one of the illegal objects of the conspiracy. If you determine that two or more conspirators agreed to accomplish one of -the illegal objects, then you may find that the conspiracy charged in Count 1 existed. If you determine that two or more conspirators agreed to accomplish more than one object of the conspiracy, then you must consider whether single or multiple conspiracies exist[ ].
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In order to prove a single conspiracy, the Government must prove that each alleged member agreed to participate in what he knew to be a collective venture directed toward a common goal. Even if the evidence shows that more than one conspiracy exists, you may still find that the conspiracy charged in Count 1 exists if it happens to be one of those conspiracies. But if you find the evidence ■proves that separate conspiracies ex-iste ], you must acquit unless you find unanimously and beyond a reasonable doubt that one of those conspiracies is the single conspiracy charged in Count 1.
The appellants claim that this instruction was erroneous because it: (1) essentially directed the jury to find that the single conspiracy charged in Count 1 existed, as long as “two or more conspirators agreed to accomplish at least one of the illegal objects of the conspiracy”; and (2) failed to instruct the jury to acquit if it found multiple conspiracies. Given the jury’s apparent difficulty distinguishing single from multiple conspiracies, the appellants argue, this instruction made it too easy for the jurors to find the single conspiracy charged in the indictment. We disagree.
The supplemental instruction was neither erroneous nor prejudicial. The district court was correct as a matter of law to charge that the government needed only to prove agreement on one of the objectives charged in the indictment in order to establish that a conspiracy existed. See United States v. Papadakis, 510 F.2d 287, 297 (2d Cir.1975). Of course, in order to obtain a conviction, the government also had to show that each defendant knowingly participated in a scheme to achieve this particular goal, see United States v. Washington, 48 F.3d 73, 80 (2d Cir.1995), but the district court made this clear in both its original and supplemental instructions.
The appellants stress that agreement on a single objective is insufficient where multiple conspiracies might exist, as here, but the district court adequately advised the jury of this possibility as well. The language of the instruction indicated that the jurors could, but were not required to, find that the single conspiracy charged in Count’ 1 existed if they found an agreement to accomplish one of the alleged criminal objectives. The district court instructed that if the jury found “that two or *114more conspirators agreed to accomplish more than one object of the conspiracy,” then it must consider whether “single or multiple conspiracies exist[],” evaluating whether “each alleged member agreed to participate in what he knew to be a collective venture directed toward a common goal.” In this way, the court focused the jury’s attention on the need to consider the possibility of multiple conspiracies. The jurors could not reasonably have been left with the impression that a simple finding of agreement on a single objective was enough to find a single conspiracy if they found agreement to accomplish other objectives as well.
The district court further instructed the jurors that, if they found multiple conspiracies, they had to acquit the defendants unless they found “unanimously and beyond a reasonable doubt that one of those conspiracies is the single conspiracy charged in Count 1.” This was correct as a matter of law, notwithstanding the appellants’ argument to the contrary. Acquittal is not automatically required if the jury finds multiple conspiracies because the jury can plausibly decide that one of those conspiracies is the single conspiracy charged in the indictment, as the court instructed here. See United States v. Tramunti, 513 F.2d 1087, 1107-08 (2d Cir.1975). Therefore, a charge should not instruct that a jury must acquit whenever it finds multiple conspiracies; acquittal is required only if the jury finds that the charged conspiracy is not one of the conspiracies that has been proved. See id. What the charge should stress is “ ‘that there must be [a] finding of the single conspiracy charged and individual knowing participation by each individual in it.’ ” United States v. Aracri, 968 F.2d 1512, 1520 (2d Cir.1992) (quoting Tramunti, 513 F.2d at 1108). The original and supplemental charges in this case adequately emphasize these points. Accordingly, the district court did not err in declining to instruct the jury simply to acquit if it found multiple conspiracies.
Given that the district judge instructed the jury on single versus multiple conspiracies, that her instructions were correct as a matter of law, that she specifically directed the jurors to consider both sets of instructions, and that the jury had those instructions at its disposal during its deliberations, we believe the jury was sufficiently well-informed to decide whether or not the government had established the existence of the single conspiracy charged in Count 1.
Second, the evidence was sufficient to support the jury’s finding of the conspiracy charged in the indictment. Whether the government’s proof shows a single conspiracy or multiple conspiracies “is a question of fact for a properly instructed jury.” United States v. Johansen, 56 F.3d 347, 350 (2d Cir.1995). We have already established that the jurors in this case were properly instructed. Their verdict must be upheld
if the evidence, viewed in the light most favorable to the government, could have led a reasonable juror to conclude beyond a reasonable doubt (1) that the scope of the criminal enterprise proven fits the pattern of the single conspiracy alleged in the indictment, and (2) that [each] defendant participated in the alleged enterprise with a consciousness of its general nature and extent.
United States v. Rosa, 11 F.3d 315, 340 (2d Cir.1993) (internal quotation marks omitted).
[I]n order to prove a single conspiracy, the government must show that each alleged member agreed to participate in what he knew to be a collective venture directed toward a common goal. The coconspirators need not have agreed on the details of the conspiracy, so long as they agreed on the essential nature of the plan.
United States v. Maldonado-Rivera, 922 F.2d 934, 963 (2d Cir.1990) (internal quotation marks and citations omitted). Moreover, “a single conspiracy is not transformed into multiple conspiracies merely *115by virtue of the fact that it may involve two or more phases or spheres of- operation, so long as there is sufficient proof of mutual dependence and assistance.” Id. In the context of narcotics operations, for example, we have held that even where there are multiple groups within an alleged conspiracy, a single conspiracy exists where the groups share a common goal and depend upon and assist each other, and we can reasonably infer that “each actor was aware of his part in a larger organization where others performed similar roles.” United States v. Bertolotti, 529 F.2d 149, 154 (2d Cir.1975).
We believe that the evidence, taken in the light most favorable to the government, supports the jury’s finding of a single conspiracy: (1) all the schemes served the same overriding goal of underwriting the needs of New Square’s community institutions; (2) the schemes were led by the same core group of community leaders, including Chaim Berger and several unin-dicted co-conspirators; (3) the schemes shared common participants, including the appellants; (4) the frauds were mutually interdependent (e.g., fraudulent documents from one scheme supported the frauds against other agencies); and (5) the conspirators used the same distinctive methods and means in their different frauds. These means and methods included the creation of sham organizations, the submission of fraudulent documentation to establish the eligibility of New Square residents and others to participate in public funding programs, the opening of special bank accounts to collect and conceal fraudulently obtained funds, and the use of nominee names, abases, and religious organizations to conceal income.
The appellants’ attempts to analogize their case to the conspiracies charged in Berger v. United States, 295 U.S. 78, 55 S.Ct. 629, 79 L.Ed. 1314 (1935), and Kotteakos v. United States, 328 U.S. 750, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946), are unavailing. In both of those cases, the defendants were charged with a single conspiracy but convicted based on evidence that established multiple conspiracies as a matter of law. See Kotteakos, 328 U.S. at 755, 66 S.Ct. 1239; Berger, 295 U.S. at 80, 55 S.Ct. 629. Both cases involved “wheel” conspiracies — multiple conspiracies of a similar nature linked by a common participant. The appellants attempt to fit this case into that box by portraying the charged conduct as multiple, separate frauds on various government agencies, bnked only by the happenstance of common methods of operation and the omnipresence of Chaim Berger as mastermind. They ignore other features linking these schemes, such as their common purpose, overlapping participants, and mutual dependence. The jury could reasonably have inferred that all of the appellants were aware of the general nature and extent of the larger, conspiracy — even though they did not each join in every aspect of the fraud — from, among other things, the substantial overlap of members in the various schemes (e.g., all four appellants in the DOE fraud, everyone but Goldstein in the HUD and IRS frauds) and the substantial interconnection of the schemes (e.g., much of the fraud against HUD involved the concealment of money from the DOE fraud).
Third, even if the proof showed multiple conspiracies, we do not think the appellants could show substantial prejudice based on this variance. In evaluating prejudice in this context, we consider:
(1) whether the trial court gave a jury charge, pursuant to Pinkerton v. United States, 328 U.S. 640, 66 S.Ct. 1180, 90 L.Ed. 1489 (1946), allowing the defendant to be convicted for substantive offenses committed by another; (2) whether statements of persons not in a conspiracy with the defendant were used against him; (3) whether there was a prejudicial “spillover” because of a large number of improperly joined defendants; and (4) whether shocking or inflammatory evidence came in against the defendant.
*116Johansen, 56 F.3d at 851. While the district court in this case gave a Pinkerton charge, consideration of the third and fourth factors cited above militates strongly against a finding of substantial prejudice.
Most importantly, any prejudicial spillover was limited, given the relatively small number of defendants and the fact that most or all of them were involved in the major frauds (against the DOE and HUD). As we have acknowledged, “the possibility of prejudice resulting from a variance increases with the number of defendants tried and the number of conspiracies proven.” Bertolotti, 529 F.2d at 156. In this respect, this case much more closely resembles Berger, in which the Supreme Court found the variance between charge and proof to be non-fatal, than Kotteakos, in which the Court found prejudice. In both cases, multiple similar conspiracies were linked primarily by a single common participant. But Berger involved only two separate counterfeiting conspiracies with two and three participants, respectively. See 295 U.S. at 80, 55 S.Ct. 629. Kotteakos, by contrast, involved eight separate conspiracies to defraud the Federal Housing Administration, with thirty-two individuals charged in the indictment and nineteen defendants at trial. See 328 U.S. at 752-53, 66 S.Ct. 1239. This case involved only two major schemes — with substantial overlapping membership — six indicted individuals, and four defendants at trial. Accordingly, the likelihood of any prejudicial spillover was relatively low.
Moreover, the most inflammatory evidence concerned the DOE fraud, in which all the appellants were involved to varying degrees, and would have been admissible in a case concerning solely that scheme. The evidence that Stern, Elbaum, and Goldstein were knowingly involved in the DOE fraud was extensive: Stern and Goldstein actively participated in misleading the ACCET, while Elbaum controlled the TYY bank account. Berger’s participation, while less pronounced, was still measurable and knowing, as addressed more fully below. See infra Part II. In sum, even assuming that the proof at trial conclusively established multiple conspiracies, which we doubt, the appellants were not substantially prejudiced by this variance.
II. Berger’s Convictions
Berger argues that his convictions should be reversed on the grounds that: (a) the evidence was insufficient to sustain his conspiracy conviction; and (b) there was a constructive amendment of the wire fraud charge against him. We disagree.
A. Sufficiency of the evidence on the conspiracy count
Berger contends that his conviction on Count 1 must be reversed because there was insufficient evidence: (1) that he knowingly participated in the DOE fraud; and (2) that his fraud on HUD was perpetrated in concert with others. When reviewing a conviction for sufficiency of the evidence, we must assess the evidence in the light most favorable to the government, crediting all inferences in its favor. See United States v. Moore, 208 F.3d 411, 413 (2d Cir.2000) (per curiam). However, evidence that is “at least as consistent with innocence as with guilt” is insufficient to support a guilty verdict. United States v. D’Amato, 39 F.3d 1249, 1256 (2d Cir.1994) (internal quotation marks omitted).
The evidence at trial was sufficient to support a jury determination that Berger knowingly participated in the DOE fraud. The evidence established that he was identified as a TYY “mentor” in materials submitted to ACCET; he claimed to be employed by TYY in letters submitted in support of various Section 8 applications; he was issued checks in his own name and in Cheindel Bernat’s name from a TYY bank account; and classrooms in the elementary school where he taught — in the same building in which the TYY Seminary was purportedly located — were used as fake offices and “mentor rooms” during *117the ACCET visits. Berger contends that this evidence is just as consistent with innocence as with guilt because there was no proof that he authorized the use of his name on the TYY employment roster, and he identified TYY as his employer and received checks from TYY because he was employed by TYY elementary school, a legitimate educational institution. However, drawing all inferences in the government’s favor, the proof as a whole suggests that Berger knowingly took part in the DOE fraud, though perhaps in a more minor capacity than the other appellants (which would explain why his name was “hardly ever mentioned” during testimony about the fraud, Appellant Berger’s Br. at 21).
Since Berger knowingly participated in the DOE fraud, we need not consider whether there was sufficient evidence to link his HUD fraud to the larger conspiracy. We note, however, that while the government’s case on this point is somewhat weaker, the evidence was sufficient to support a jury determination that Berger’s HUD fraud' was linked to the larger conspiracy, given the “strikingly parallel behavior” of the conspirators engaged in Section 8 fraud, United States v. Turoff, 853 F.2d 1037, 1045 (2d Cir.1988), and Berger’s use of an account in Cheindel Bernat’s name to receive proceeds from the DOE and HUD frauds and to conceal income from the IRS.
B. Constructive amendment of the wire fraud charge
Berger contends that the government’s proof at trial constructively amended the charge in Count 7 that he perpetrated a wire fraud against HUD. The “to wit” clause of Count 7 mistakenly stated that Berger fraudulently caused funds to be wired to the New Square Housing Authority on the basis of false information about his income. In fact, the proof at trial established that: (1) Berger’s Section 8 subsidies as a tenant — which were inflated as a result of the understatement of his income — came from the Spring Valley Housing Authority; and (2) his fraud with respect to the New Square Housing Authority involved the concealment of his ownership of a house, not misrepresentations about his income. •
In order to prevail on his claim of constructive amendment, Berger must show that the proof at trial “so altered an essential element of the charge that, upon review, it is uncertain whether the defendant was convicted of conduct that was the subject, of the grand jury’s indictment.” United States v. Frank, 156 F.3d 332, 337 (2d Cir.1998) (per curiam). No constructive amendment occurs “where a generally framed indictment encompasses the specific legal theory or evidence used at trial.” United States v. Wallace, 59 F.3d 333, 337 (2d Cir.1995). (internal quotation marks omitted). Accordingly, we have “consistently permitted significant flexibility in proof, provided that the defendant was given notice of the core of criminality to be proven at trial.” United States v. Patino, 962 F.2d 263, 266 (2d Cir.1992) (internal quotation marks omitted). As the district court noted, constructive amendment is typically found where the government offers proof of offenses or transactions not even mentioned in the indictment.
Under these standards, no constructive amendment occurred here because there can be little doubt that Berger was fully informed of the nature of the charges against him and was convicted of the crimes with which he was charged. The count in question incorporated paragraphs 82 arid 83 of the indictment by reference, and these paragraphs indicated that the wire fraud the government intended to prove involved both Berger’s fraudulent collection of Section 8 subsidies as a shadow landlord from the New Square Housing Authority and his fraudulent understatement of income so as to collect greater Section 8 subsidies as a tenant from the Spring Valley Housing Authority. Ample evidence was presented that Berger *118had adequate notice that the government intended to prove both of these frauds. Before trial, the government represented to the district court — with copies to all opposing counsel — that Count 7 charged Berger with participating in two separate frauds through the use of the wires. Moreover, in ruling on Berger’s motion to dismiss Count 7, the district court confirmed that “the Government has indicated its intent to prove either or both of the[ ] two sets of transactions” listed in paragraphs 82 and 83 of the indictment.
Meanwhile, the error in the “to wit” clause did not lead Berger to be tried for crimes not charged by the grand jury. Berger claims that the indictment lacked a valid allegation of a wire transfer to or from the Spring Valley Housing Authority even though he may have been convicted for a wire fraud involving that particular entity. We disagree. The count included all of the essential elements of wire fraud. See United States v. Zagari, 111 F.3d 307, 327 (2d Cir.1997). At worst, the text of the count itself failed to list all of the victims and other specifics of Berger’s alleged wire fraud against HUD, and this oversight was addressed elsewhere in the indictment. In the final analysis, all of the transactions the government ultimately proved at trial were contained in the indictment.
III. Goldstein’s Convictions
Goldstein argues that his convictions should be reversed on the ground that he withdrew from the conspiracy in 1991, and thus most of the charges against him were barred by the statute of limitations. We believe that the jury was entitled to find that Goldstein’s resignation from TYY was insufficient to constitute withdrawal from the conspiracy.
On August 1, 1991, Goldstein sent a resignation letter to Chaim Berger, with a copy to ACCET, stating that he was leaving TYY, effective September 1, to pursue a new opportunity. Goldstein claims that this letter provides conclusive evidence that his involvement in the charged criminal conduct had ended by September 1, 1991. The statute of limitations for most of the charges against Goldstein was five years. See 18 U.S.C. § 3282. Therefore, Goldstein argues, since he withdrew from the criminal activity more than five years before the indictment was filed, he was entitled to judgments of acquittal on most of the charges against him.
We think that Goldstein has failed to establish adequate withdrawal as a matter of law. The evidence supports the jury’s apparent conclusion that Gold-stein’s resignation did not amount to a disavowal of the conspiracy. It is well-established that
[m]ere cessation of activity is not enough to start the running of the statute; there must also be affirmative action, either the making of a clean breast to the authorities, or communication of the abandonment in a manner reasonably calculated to reach co-conspirators. And the burden of establishing withdrawal lies on the defendant.
United States v. Borelli, 336 F.2d 376, 388 (2d Cir.1964) (internal quotation marks and citation omitted). Our case law strongly suggests that resignation from a criminal enterprise, standing alone, does not constitute withdrawal as a matter of law; more is required. Specifically, the defendant must not take any subsequent acts to promote the conspiracy, see United States v. Nerlinger, 862 F.2d 967, 974 (2d Cir.1988) (resignation plus actions that “disabled [defendant] from further participation” in the conspiracy established withdrawal); United States v. Goldberg, 401 F.2d 644, 649 (2d Cir.1968) (resignation plus the absence of any subsequent activity in furtherance of the conspiracy established withdrawal), and must not receive any additional benefits from the conspiracy, see United States v. Eisen, 974 F.2d 246, 269 (2d Cir.1992) (no withdrawal where defendant resigned from corrupt law firm but continued to receive a per*119centage of recoveries). We agree with the Third Circuit’s more explicit statement of these principles:
(1) resignation from the enterprise does not, in and of itself, constitute withdrawal from a conspiracy as a matter of law;
(2) total severing of ties with the enterprise may constitute withdrawal from the conspiracy; however (3) even if the defendant completely severs his or her ties with the enterprise, the defendant still may remain a part of the conspiracy if he or she continues to do acts in furtherance of the conspiracy and continues to receive benefits from the conspiracy’s operations.
United States v. Antar, 53 F.3d 568, 583 (3d Cir.1995).
Under these standards, the question of withdrawal was properly submitted to the jury, and there was adequate evidence to support the jury’s apparent rejection of Goldstein’s withdrawal defense. Although Goldstein purported to resign from TYY in 1991, he did not fully abandon the conspiracy in the ensuing years. First, as the government notes, his very resignation letter helped to further the conspiracy, since it “repealed] the very lies upon which the Pell Grant fraud was grounded” and was forwarded to ACCET, the entity responsible for assessing TYY’s eligibility to participate in the program. Second, Goldstein failed to take any steps as an ACCET Trustee to inform ACCET that TYY did not exist. While withdrawal does not require a defendant to turn in his co-conspirators or warn off possible victims,' Gold-stein’s failure to advise ACCET plainly advanced the goals of the conspiracy and, at the very least, suggested that he had not renounced these goals. Finally, in 1996, Goldstein lied to law enforcement agents by falsely stating that he had worked as TYY’s Administrator, falsely identifying other supposed administrators, and falsely describing the supposed educational offerings at the sham school.Even if Goldstein truly severed all ties' to the conspiracy after his resignation in 1991, these lies — which occurred well within the five-year period preceding the filing of the indictment — reestablished his link by helping to conceal the conspiracy from investigators.
IV. Batson Claim
According to the appellants, the district court erred in rejecting their Bat-son claim based on the prosecutor’s use of a peremptory, challenge to strike a Jewish prospective juror. In our view, however, the district court properly rejected the claim because the government offered a nondiscriminatory explanation for the disputed challenge and the appellants failed to prove purposeful discrimination.
During jury selection, the prosecutor exercised a peremptory challenge to strike a prospective juror who wore a yarmulke, identified himself as “an observant Jew,” and advised the court that he was a rabbi. Defense counsel raised a Batson objection. According to the prosecutor, the basis for the challenge was the Rabbi’s expertise: “When this jury, is deliberating, . -.. presumably they will be considering, given the nature of the charges in this case, the question of Jewish education, where it takes place, how it-takes place.... [T]hey will turn to [the- juror in question] as an expert.... [H]e’s going to carry undue influence.” The district court found that the government had proffered a religion-neutral reason for its. challenge, even though the judge herself found the government’s rationale less compelling than concerns, about the Rabbi’s fairness (based on the opinions about Orthodox Jews he had expressed in a written questionnaire).
In Batson v. Kentucky, 476 U.S. 79, 89, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986), the Supreme Court established that prosecutors may not exercise peremptory strikes on the basis of race. The Court has since extended this prohibition to strikes on the basis of sex. See J.E.B. v. Alabama ex rel. T.B., 511 U.S. 127, 140-43, 114 S.Ct. 1419, 128 L.Ed.2d 89 (1994). Criminal defendants also are prohibited *120from exercising discriminatory peremptory strikes. See Georgia v. McCollum, 505 U.S. 42, 59, 112 S.Ct. 2348, 120 L.Ed.2d 33 (1992). The Court has not explicitly extended Batson to religion-based peremptory challenges, and the lower courts are divided on the question. Compare United States v. Somerstein, 959 F.Supp. 592, 595 (E.D.N.Y.1997) (extending Batson to religion-based challenges), with State v. Davis, 504 N.W.2d 767, 771 (Minn.1993) (refusing to extend Batson).
The appellants contend that Bat-son should logically apply to a challenge allegedly based on a juror’s religion. We need not reach this question here. Even assuming that Batson applies, the prosecutor provided a nondiscriminatory explanation for striking the Rabbi: his expertise. The government need only provide “an explanation based on something other than” the juror’s membership in the protected class. Hernandez v. New York, 500 U.S. 352, 360, 111 S.Ct. 1859, 114 L.Ed.2d 395 (1991). Contrary to the appellants’ contentions, the government did not strike the Rabbi because of his general religious experiences and knowledge, but rather because of his particular familiarity with Jewish educational institutions, the very subjects of the case against the appellants. Accordingly, the district court did not clearly err in determining that the prosecutor was not acting with discriminatory intent in exercising this challenge.
V. Enhancement for Misrepresentation of Affiliation with an Educational Institution
At sentencing, the district court decided to apply U.S.S.G. § 2Fl.l(b)(4)(A), which provides a two-level enhancement where “the offense involved ... a misrepresentation that the defendant was acting on behalf of a[n] ... educational ... organization.” We believe the district court did not err by enhancing the appellants’ sentences on this basis.
“We use basic statutory construction rules when interpreting the Guidelines.” United States v. Martinez-Santos, 184 F.3d 196, 204 (2d Cir.1999). “Therefore, we must give the words used their common meaning, absent a clearly expressed manifestation of contrary intent.” United States v. Demerritt, 196 F.3d 138, 141 (2d Cir.1999) (internal quotation marks omitted). We agree with the district court’s conclusion that the plain language of the Guideline applies to the behavior of the appellants, since they misrepresented to government agencies that they were affiliated with TYY, a “completely fictitious” educational organization.
According to the appellants, the supporting materials to the Guideline suggest that the enhancement should apply only where a defendant exploits the altruism of private individuals, not where he simply defrauds government agencies. Application Note 5 to § 2F1.1 provides several examples of conduct to which subsection (b)(4)(A) would apply, all of which involve misrepresentations to private individuals. In addition, the Background Notes suggest that the enhancement is meant to punish “defendants who exploit victims’ charitable impulses or trust in government” because such actions “create particular social harm.”
Nevertheless, we do not think these supporting materials “clearly express[]” an intent that § 2F1.1(b)(4)(A) not apply in this case. Demerritt, 196 F.3d at 141. The commentators “could not have intended” the examples in the Application Notes “to be exhaustive,” United States v. Ferrera, 107 F.3d 537, 541 (7th Cir.1997), especially since they wrote that conduct to which the enhancement applies “would include” the examples they listed, U.S.S.G. § 2F1.1 Application Note 5, not that such conduct was limited to those examples. See United States v. Bennett, 161 F.3d 171, 191 (3d Cir.1998) (“This list of examples is illustrative, not exhaustive.”), cert. denied, — U.S. -, 120 S.Ct. 61, 145 L.Ed.2d 53 (1999). Moreover, the specific *121purposes outlined in the Background Notes are arguably implicated on these facts, since the appellants took advantage of the government’s generosity, thereby defrauding the taxpayers as a whole rather than any particular one of them.
The text of § 2Fl.l(b)(4)(A) plainly focuses on the nature and context of the misrepresentation, not the identity of the victim. We see no persuasive reason to look beyond this plain meaning, nor do we think the supporting materials' on which the appellants rely counsel a different result.
CONCLUSION
For the foregoing reasons, we conclude that: (1) the appellants were properly convicted of the conspiracy charged in the indictment, as the evidence was sufficient to support a jury finding of a single conspiracy; (2) Berger’s convictions should be upheld since there was sufficient evidence of his knowing participation in the conspiracy and no constructive amendment of the wire fraud charge against him; (3) Gold-stein’s convictions should be upheld because he did not establish withdrawal from the conspiracy as a matter of law; (4) the district court properly rejected the appellants’ Batson claim; and (5) the court properly enhanced the appellants’ sentences for misrepresentation of affiliation with an educational institution. Accordingly, we affirm the district court’s judgments against all four appellants in every respect.