Defendant-appellant Luis Manuel Rodriguez-Lara (“Rodriguez”), an alien convicted of reentry after deportation, appeals the district court’s denial of his motion to appoint an expert to assist him in pursuing his equal protection and fair cross-section challenges to the composition of the jury pool in the Fresno Division of the Eastern District of California. Rodriguez also claims that the district court erred in its application of the U.S. Sentencing Guidelines and that the court violated his Sixth Amendment rights by enhancing his sentence in violation of Apprendi v. New Jersey and its progeny.

Given the extent of the fair cross-section showing Rodriguez was able to develop even without the help of an expert, we hold that under the circumstances reasonably competent counsel would have required the services of an expert for a paying client, and the lack of an expert prejudiced Rodriguez. The district court therefore abused its discretion in denying Rodriguez’s motion for the appointment of an expert. Although Rodriguez’s Sixth Amendments rights were not violated by the judge’s use of a prior conviction to enhance Rodriguez’s sentence, the district court committed plain error in applying the acceptance-of-responsibility reduction under the Sentencing Guidelines. We therefore vacate Rodriguez’s sentence and remand for resentencing and the appointment of an expert.

I. BACKGROUND

Under the Jury Selection and Service Act of 1968 (JSSA), 28 U.S.C. § 1861 et seq., each federal judicial district must devise a plan for random selection of grand and petit jurors. This plan must be designed to ensure that litigants have grand and petit juries selected from a fair cross-section of the community in the applicable district or division of the district, and that no prospective jurors are subject to discrimination on any of several enumerated grounds. Id. §§ 1861-63. The statute contemplates that each district or division will use voter registration lists or the lists of actual voters of the political subdivisions within that district or division, but the statute also requires that jury selection plans “prescribe some other source or sources of names in addition to voter lists where necessary to foster the policy and protect the rights” of fair cross-section and anti-discrimination. Id. § 1863(b)(2).

The jury plan for the Eastern District of California provides that names of prospective jurors for the master jury wheel are to be drawn randomly from voter registration records for all counties within the relevant division of the district. Amended Plan for the Random Selection of Grand and Petit Jurors, General Order No. 374 (E.D.Cal. Mar. 22, 2000), at 3 (hereinafter “Amended Plan”). The Fresno Division consists of Merced, Mariposa, Madera, Fresno, Inyo, Kings, Tulare, Kern, Calav-eras, Stanislaus, and Tuolumne Counties. Id. at 1. Names from the master jury wheel are drawn randomly as necessary to fill the qualified jury wheel (which consists of the names of individuals eligible for jury service and not exempt or excused); names from the qualified wheel are drawn randomly as necessary to select the individuals to be summoned for service on grand and petit juries. Id. at 8, 12. The qualifications for service are: United States citizenship; eighteen years of age; residence within the judicial district for one year; ability to read, write and understand English; ability to speak English; mental and physical capability to render satisfactory service; and no charge pending or conviction for a crime punishable by imprisonment for more than one year (absent restoration of civil rights). Id. at 10; 28 U.S.C. § 1865 (b). Members of the armed forces in active service, members of police and fire departments, and public officers actively engaged in the performance of their official duties are exempt from service. Amended Plan at 11; 28 U.S.C. § 1863 (b)(6). Individuals who are over seventy years of age, who have served as a federal grand or petit juror within the preceding two years, who serve as volunteer safety personnel, or for whom service would constitute an “undue hardship or extreme inconvenience” (for example, because of distance from the court or family emergency), may be excused from service. Amended Plan at 10-11.

In March 2003, Rodriguez was charged with being a deported alien found in the United States in violation of 8 U.S.C. § 1326 . After successfully moving to represent himself, Rodriguez moved to dismiss the indictment, claiming that Hispanics were underrepresented in the jury wheel of the Fresno Division of the Eastern District of California, in violation of the fair cross-section requirement of the Sixth Amendment and of the equal protection guarantee of the Fifth Amendment. Relatedly, Rodriguez moved the court to provide him with jury statistics compiled by the court on forms designated “JS-12” (commonly known simply as “JS-12s”), and to appoint a demographic expert to assist him in substantiating his claims concerning the systematic underrepresentation of Hispanics in the jury pool.

The court denied these motions without prejudice, and Rodriguez renewed them, this time attaching supporting exhibits including (in relevant part) a 1992 declaration prepared for another case by an expert involved in several jury under-representation cases; the 1992 jury selection plan for the Eastern District of California; several JS-12s from the early 1990s; and 2000 census population data for the Fresno Division. The district court expressed doubt about the viability of Rodriguez’s claims but nonetheless ordered that Rodriguez be provided with a more recent JS-12.

Three days later, Rodriguez again renewed his motion to dismiss, now including the 2003 JS-12 statistics (provided by the court) reflecting demographics both for the group of individuals who returned juror questionnaires after being drawn from the master jury wheel, and for the group of individuals placed into the qualified jury wheel. Using this data, Rodriguez alleged a substantial disparity between the proportion of Hispanics in the subset of the population old enough to serve on federal juries (the “age-eligible” population) and the proportion of Hispanics in the qualified jury wheel. Incorporating some of the arguments from the expert declaration he had attached to his second motion, Rodriguez asserted that the reason for the disparity was the Fresno Division’s use of voter lists as the sole source of names for the master jury wheel.

The day before trial, the court denied Rodriguez’s motions for the final time. In the view of the district court, Rodriguez was required to show a disparity between Hispanic representation in the qualified jury wheel and Hispanic representation in the subset of the population meeting all the federal juror-eligibility requirements (the “jury-eligible population”), not merely the general or age-eligible population, and the court characterized the government’s “supplemental voter information exhibit” as showing that for a portion of the Fresno Division, the jury-eligible population was approximately 17% Hispanic even though the total population was approximately 30% Hispanic. The court noted that challenges to jury pool composition in the Eastern District of California had been rejected by the Ninth Circuit in 1996 and by the Eastern District in 2003. According to the court, the “best way” to determine if Rodriguez’s fair cross-section and equal protection rights were being violated “is to see who shows up tomorrow in the jury panel. And we will get a very good look. And if you don’t believe that there is a fair representation there, you can object and if it isn’t a representative panel, we don’t have to proceed to trial.” The court further observed that “in the last 15 to 20 cases, we get very, very strong Hispanic representation.” Not “see[ing] anything more that has been submitted than when we started this process,” and because of “the insufficiency of the factual showing which didn’t require an expert,” the court denied Rodriguez’s motions to dismiss and to have an expert appointed.

Rodriguez was convicted after a one-day trial.

At sentencing, the court applied a 16-level enhancement because Rodriguez had been previously deported following a conviction for a drug trafficking offense — a state felony conviction for transport of methamphetamine — for which he had received a sentence greater than 13 months. See U.S. Sentencing Guidelines Manual § 2L1.2(b)(l)(A)(I) (2002). After Rodriguez expressed deep regret for returning to the United States, the court gave a two-level reduction for acceptance of responsibility under U.S.S.G. § 3El.l(a), but declined to give a third level because the case went to trial and therefore the acceptance of responsibility was not timely (though the judge denied that he was penalizing Rodriguez for going to trial). Rodriguez did not object to the judge’s failure to give a three-level reduction. Applying the resulting sentencing range, the court sentenced Rodriguez to 77 months imprisonment, along with a special assessment of $100 (waived) and three years of supervised release.

Rodriguez timely appealed, and we have jurisdiction under 28 U.S.C. § 1291 .

II. ANALYSIS

A. Jury Composition Challenges/Failure to Appoint an Expert

A district court’s denial of a request for public funds to hire an expert is reviewed for abuse of discretion. United States v. Nelson, 137 F.3d 1094 , 1101 n. 2 (9th Cir.1998). A challenge to the composition of grand or petit juries is reviewed “independently and non-deferentially.” Thomas v. Borg, 159 F.3d 1147, 1149 (9th Cir.1998) (citation and internal quotation marks omitted).

Federal law provides that a district judge shall authorize the provision of expert services to a defendant financially unable to obtain them where such services are necessary for adequate representation. 18 U.S.C. § 3006A(e)(l). It is an abuse of discretion to deny a request for an expert under this provision where (1) “reasonably competent counsel would have required the assistance of the requested expert for a paying client,” and (2) the defendant “was prejudiced by the lack of expert assistance.” Nelson, 137 F.3d at 1101 n. 2 (citation and internal quotation marks omitted). Prejudice must be shown by clear and convincing evidence. Id. Therefore, Rodriguez’s claim that an expert should have been appointed must be evaluated in the context of the underlying claims for which he asserts he ought to have been given expert help.

Rodriguez’s two challenges to the representativeness of the Fresno Division jury pool are related but distinct. In Castaneda v. Partida, 430 U.S. 482 , 97 S.Ct. 1272 , 51 L.Ed.2d 498 (1977), the Supreme Court laid out the following procedure for making out a prima facie ease for an equal protection violation in the jury selection procedures:

Id. at 494 , 97 S.Ct. 1272 (citations omitted). These elements, if shown, raise the inference of discriminatory intent: “Once the defendant has shown substantial underrepresentation of his group, he has made out a prima facie case of discriminatory purpose.” Id. at 495 , 97 S.Ct. 1272 . At that point, “the burden of proof shifts to the State to rebut the presumption of unconstitutional action by showing that permissible racially neutral selection criteria and procedures have produced the monochromatic result.” Id. at 494 , 97 S.Ct. 1272 (citation and internal quotation marks omitted).

To establish a prima facie case for a violation of the Sixth Amendment’s fair cross-section requirement, under Duren v. Missouri, 439 U.S. 357 , 99 S.Ct. 664 , 58 L.Ed.2d 579 (1979), the defendant must show:

Id. at 364 , 99 S.Ct. 664 . Unlike the equal protection challenge, the fair cross-section claim does not require a showing that the selection procedure is susceptible of abuse or not race-neutral; the defendant must only show that the exclusion of his or her group is “systematic.” Once the defendant has established a prima facie case, the burden shifts to the government to show that “a significant state interest be manifestly and primarily advanced by those aspects of the jury-selection process ... that result in the disproportionate exclusion of a distinctive group.” Id. at 367-68 , 99 S.Ct. 664 ; see also Thomas, 159 F.3d at 1150 .

The selection of a grand or petit jury in violation of either the equal protection or the fair cross-section guarantee is structural error that entitles a defendant to relief without a demonstration of prejudice. See Vasquez v. Hillery, 474 U.S. 254, 263-64, 106 S.Ct. 617 , 88 L.Ed.2d 598 (1986) (plurality and majority portions); United States v. Okiyama, 521 F.2d 601, 604 (9th Cir.1975) (per curiam); see also Taylor v. Louisiana, 419 U.S. 522, 530 , 95 S.Ct. 692 , 42 L.Ed.2d 690 (1975) (describing the fair cross-section requirement as “fundamental to the jury trial guaranteed by the Sixth Amendment”).

1. Fair Cross-Section

We begin with the Sixth Amendment claim. Rodriguez’s claim clearly satisfies the first prong of Duren . Hispanics have long been recognized as a “distinctive” group in the community. See United States v. Sanchez-Lopez, 879 F.2d 541, 547 (9th Cir.1989) (citing Castaneda, 430 U.S. at 495 , 97 S.Ct. 1272 ).

The second prong of the Duren test requires the defendant to show that the distinctive group is underrepresented in jury venires “in relation to the number of such persons in the community.” Duren, 439 U.S. at 364 , 99 S.Ct. 664 . This standard seems clear enough — it is to the community that comparisons must be made for the purposes of a fair cross-section claim. Here, however, the district court faulted Rodriguez’s showing — which compared jury pool Hispanic representation to Hispanic representation in the age-eligible population — for failing to make a comparison to Hispanic representation in the jury-eligible population.

The weight of Supreme Court and circuit authority teaches that, for purposes of the prima facie case, the proportion of the distinctive group in the jury pool is to be compared with the proportion of the group in the whole community. In Duren itself, the Supreme Court required the defendant to show “that the representation of this group in venires from which juries are selected is not fair and reasonable in relation to the number of such persons in the community.” Id. (emphasis added). The Court then elaborated that “the fair-cross-section requirement involves a comparison of the makeup of jury venires or other sources from which jurors are drawn with the makeup of the community, not of voter registration lists.” Id. at 365 n. 23, 99 S.Ct. 664 (emphasis in original). Noting that no evidence in the record undermined the numbers proffered by the defendant, the Supreme Court evaluated the defendant’s prima facie case using census data showing the proportion of age-eligible members of the distinctive group at issue. Id. at 364 n. 21, 365 & n. 23, 99 S.Ct. 664 . The Supreme Court has subsequently reiterated that “[t]he second prong of Duren is met by demonstrating that the [distinctive] group is underrepresented in proportion to its position in the community as documented by census figures.” Teague v. Lane, 489 U.S. 288 , 301 n. 1, 109 S.Ct. 1060 , 103 L.Ed.2d 334 (1989) (plurality portion) (emphasis added).

Other Supreme Court authority reflects a similarly permissive view of the requirements of a prima facie showing of underrepresentation. In Castaneda , for example, the Supreme Court allowed the defendant to use total population figures to establish a prima facie case in the related context of an equal protection challenge to jury composition. 430 U.S. at 495-96 , 97 S.Ct. 1272 . Similarly, in Turner v. Fouche, 396 U.S. 346 , 90 S.Ct. 532 , 24 L.Ed.2d 567 (1970), the Supreme Court evaluated the representativeness of a grand jury source list by comparison with minority representation within the general population of the relevant county. Id. at 359 , 90 S.Ct. 532 . And in Alexander v. Louisiana, 405 U.S. 625 , 92 S.Ct. 1221 , 31 L.Ed.2d 536 (1972), the Supreme Court analyzed a prima facie case for an equal protection violation using census data reflecting the proportion of the dis tinctive group among the age-eligible population, whom the Court characterized as “presumptively eligible for grand jury service,” even as it acknowledged that state law disqualified potential jurors based on non-residency, illiteracy, alien-age, disability, and criminal history, as well as age. Id. at 627 & n. 4, 92 S.Ct. 1221 .

Following the Supreme Court’s lead, our circuit’s fair cross-section cases treat total population figures as an appropriate basis for comparison for the purposes of a prima facie case under Duren. See, e.g., United States v. Suttiswad, 696 F.2d 645 , 648 n. 3 (9th Cir.1982); United States v. Armstrong, 621 F.2d 951, 955-56 (9th Cir.1980) (Kennedy, J.). In United States v. Sanchez-Lopez, we specifically confronted the government’s objection that a defendant’s statistical analysis based on census data did not take into account the proportion of Hispanics (the distinctive group there in question) who were ineligible for jury service. 879 F.2d at 547 . Citing Duren and Castaneda , we squarely rejected the proposition “that the defendants were required to provide jury eligible population figures.” Id. Instead, “[b]e-cause the government ... failed to present any evidence that contradicted appellants’ figures, we will assume for purposes of this analysis that the statistics are valid.” Id. This circuit has generally continued to adhere to the Duren/Sanchez-Lopez view that the defendant need not come forward with jury-eligible population data in order to make a prima facie ease. See, e.g., Randolph v. California, 380 F.3d 1133, 1140 (9th Cir.2004); Thomas, 159 F.3d at 1150 ; Nelson, 137 F.3d at 1101 .

Our case law reflects one corollary to this rule: where the record contains population data broken down by age, the representativeness of the jury pool is to be compared to this refined set of data for the purpose of the defendant’s prima facie case under Duren. See United States v. Esquivel, 88 F.3d 722, 726-27 (9th Cir.1996) (opinion of T.G. Nelson, J., announcing the judgment of the panel). Although the Supreme Court’s acceptance of comparisons using total population figures clearly indicates that a defendant is not required to gather data reflecting the age-eligible population of the distinctive group in question, see, e.g., Castaneda, 430 U.S. at 495-96 , 97 S.Ct. 1272 , our use of age-eligible data where available comports with the Supreme Court’s analysis in Duren itself, which relied on census data reflecting the proportion of the distinctive group in the adult population, see 439 U.S. at 362 , 99 S.Ct. 664 .

Two of our cases appear to be in conflict with the Supreme Court and with the Sanchez-Lopez line of cases. See United States v. Artero, 121 F.3d 1256, 1261-62 (9th Cir.1997) (requiring a fair-cross-section claimant to compile data reflecting the jury-eligible—not merely age-eligible—population in order to make the representativeness comparison for the second prong of the prima facie case); Sanders v. Woodford, 373 F.3d 1054, 1069-70 (9th Cir.2004) (following Artero ). How ever, given the overwhelming weight of our own prior case law and (more importantly) that of the Supreme Court, we must adhere to our longstanding authority that the defendant’s prima facie case for a fair-cross section claim may rely on a comparison to total population data or, where available in the record, age-eligible population data.

Sanchez-Lopez is the binding precedent of our circuit, which a three-judge panel may not overrule absent intervening Supreme Court or en banc authority (of which we have found none). See Obrey v. Johnson, 400 F.3d 691, 699-701 (9th Cir.2005) (recognizing and resolving tension among Ninth Circuit cases applying conflicting versions of the harmless error standard in civil cases); see also H & D Tire & Automotive-Hardware, Inc. v. Pitney Bowes, Inc., 227 F.3d 326, 330 (5th Cir.2000) (“When panel opinions appear to conflict, we are bound to follow the earlier opinion.”).

Under the Duren/Sanchez-Lopez approach, the data Rodriguez has presented satisfies the second prong of the prima facie case for a fair cross-section violation. Our case law has settled on “absolute disparity”- — -the difference between the percentage of the distinctive group in the community and the percentage of that group in the jury pool — as the appropriate measure of the representativeness of the jury pool. See Sanchez-Lopez, 879 F.2d at 547 . We have decline to find underrep- resentation of a distinctive group where the absolute disparity was 7.7% or lower, see Suttiswad, 696 F.2d at 649 (7.7% disparity); Thomas, 159 F.3d at 1151 (collecting cases), while we have found a 15.4% absolute disparity sufficient to satisfy the second prong of the Duren test, and cited with approval another circuit’s recognition of the significance of a 14.1% disparity, see Randolph, 380 F.3d at 1140 (citing Ramseur v. Beyer, 983 F.2d 1215, 1232 (3d Cir.1992) (en banc)).

In Rodriguez’s case, the JS-12 data and the 2000 census data for the age-eligible population show an absolute disparity of 14.55% between the percentage of age-eligible Hispanics in the Fresno Division population (35.21%) and the percentage of Hispanics in the subset of the jury pool for which ethnicity information is available (20.66%). A 14.55% absolute disparity falls within the range of disparities that we have recognized as significant for the purpose of establishing underrepresentation in the context of a prima facie case. Therefore Rodriguez has satisfied the second Duren prong.

The third Duren prong requires a showing that the underrepresentation results from a systematic exclusion of the distinctive group in the jury-selection process. Under Duren , “disproportionate exclusion of a distinctive group from the venire need not be intentional to be unconstitutional, but it must be systematic.” Randolph, 380 F.3d at 1141 . Courts have found systematic exclusion to be shown, for example, where a jury selection system allowed women to opt out of service more easily than men, where a computer error resulted in the exclusion of individuals from two regions where a large proportion of racial and ethnic minorities lived, and where jurors were selected based on wholly subjective criteria. Id. (citing Duren itself, United States v. Jackman, 46 F.3d 1240 (2d Cir.1995), and Gibson v. Zant, 705 F.2d 1543 (11th Cir.1983), for these examples). We determined that a defendant failed to satisfy the “systematic exclusion” prong where he presented a hypothesis as to the cause of Hispanic underrepresentation but “presented no evidence to support this suggestion.” Id. at 1141.

In this case, Rodriguez has claimed that systematic exclusion of Hispanics results from the Fresno Division’s use of voter registration lists as the sole source of names for its master jury wheel. In support of this contention, Rodriguez offered a 1992 declaration prepared for another case by Professor J. Dennis Willigan, a sociology professor involved in several jury underrepresentation cases, who asserted that the practice of selecting jurors from voter registration lists underrepresents racial and ethnic minorities. Rodriguez also cited People v. Harris, in which a plurality of the California Supreme Court concluded that a defendant had satisfied the “systematic exclusion” prong of Duren with a sufficient showing that underrepresentation results from the use of voter registration lists as the sole source of names for the jury pool. 201 Cal.Rptr. 782 , 679 P.2d at 446 (plurality opinion). Relatedly, the concurrence in Harris alluded to “published studies which point to the exclusive reliance upon voter registration lists as a likely source of racial and ethnic disparity in the composition of juries.” Id. at 455 (Grodin, J., concurring in the judgment).

However, Rodriguez was not able to provide evidence linking sole reliance on voter registration lists for jury selection to current systematic exclusion of Hispanics in the Fresno Division. Rodriguez’s failure of proof leaves his prima facie case unfinished.

2. Appointment of an Expert

If the issue before us were the underlying question of whether Rodriguez had made out a prima facie case for dismissing his indictment on Sixth Amendment grounds, on this record we would have to answer no. But the question we must answer is whether Rodriguez was entitled to have expert assistance to help him establish the underlying claim.

Rodriguez’s failure to complete his pri-ma facie case is not fatal to his appeal of the denial of his motion to have an expert appointed. Indeed, conditioning the entitlement to an expert on a defendant’s establishing a prima facie case would make little sense: such a rule would provide assistance to a defendant only upon a demonstration that he does not require it. Instead, we must determine whether (1) “reasonably competent counsel would have required the assistance of the requested expert for a paying client,” and (2) the defendant “was prejudiced by the lack of expert assistance.” Nelson, 137 F.3d at 1101 n. 2 (citation and internal quotation marks omitted).

Under the circumstances presented here, we conclude that both prongs of the test are satisfied. Although Rodriguez has not established a prima facie case for a fair cross-section violation, he has made a substantial showing sufficient to warrant further inquiry. Rodriguez has shown that Hispanics are substantially underrepresented in the Fresno Division jury pool, and Rodriguez has alleged (with some support, though no particularized evidence) a plausible theory of systematic exclusion: specifically, that the use of voter registration records as the sole source of names for the Fresno Division jury pool systematically underrepresents Hispanics. An expert would be able to investigate whether Hispanics have been systematically excluded and potentially provide the necessary information to complete Rodriguez’s prima facie case. This is precisely the type of situation in which reasonably competent counsel would require the services of an expert for a paying client: the defendant has alleged a dispositive defense that is supported in substantial measure by the evidence available but which cannot be fully developed without the help of an expert.

In order to demonstrate that the district court abused its discretion in failing to appoint an expert, Rodriguez must also show by clear and convincing evidence that the court’s failure to do so prejudiced him. No Ninth Circuit case appears to have addressed the prejudicial effect on a fair cross-section claim of a district court’s failure to appoint an expert.

If prejudice means that the defendant must show his defense would have been successful, then obviously Rodriguez’s claim must fail. However, such a narrow understanding would put nearly all defendants in a catch-22 and reduce the statutory provision for federal funding for expert services to an empty promise: the expert’s services would only be available upon the showing of a meritorious defense, and the defense could only be shown with the help of an expert.

In the few cases in which we have had occasion to elaborate on the meaning of the standard of 18 U.S.C. § 3006A(e), we have rejected this narrow understanding. In United States v. Hartfield, 513 F.2d 254 (9th Cir.1975), abrogated on other grounds, United States v. Sneezer, 900 F.2d 177 , 179 n. 3 (9th Cir.1990), for example, we held that the denial of defendant’s motion to obtain an electroencephalogram (EEG) was an abuse of discretion “because the only defense available to [Hartfield] was a defense that turned on his mental condition.” Id. at 258 . We did not require the defendant to show that an EEG would have provided a successful defense. Similarly, in United States v. Bass, 477 F.2d 723 (9th Cir.1973), we held that the district court’s failure to appoint a psychiatric expert for the defense was an abuse of discretion because the defendant’s “family and personal history indicated that an insanity defense might be appropriate.” Id. at 725 . In that case, the defendant was entitled to an expert notwithstanding our acknowledgment that “we cannot predict the outcome of an examination conducted by [the requested] expert.” Id. at 726 . By contrast, in United States v. Labansat, 94 F.3d 527 (9th Cir.1996), we held that a bank robbery defendant was not prejudiced by the district court’s refusal to authorize public funding for the hiring of an expert on eyewitness identification to discredit prosecution witnesses, because the evidence against the defendant was overwhelming: numerous witnesses identified the defendant as the robber, the defendant’s vehicle was at the scene of the crime, the gloves worn by the robber were found in the defendant’s possession, and the jury saw bank surveillance photographs of the robber, who was identified as the defendant by his own sister. Id. at 529-30 .

These cases illustrate that the function of the prejudice inquiry is to prevent appellate courts from second-guessing district judges in cases in which the requested services could not have mattered to the outcome, not to force the defendant to prove that the requested expenditure would necessarily have produced a different result. Thus, while the wealth of evidence against the defendant in Labansat demonstrated that the denial of expert assistance did not prejudice him, the court’s inability to predict what the expert services requested in Hartfield and Bass would reveal did not foreclose relief in those cases.

The circumstances here resemble those in Hartfield and Bass . Like the defendants in those cases, Rodriguez has requested expert services in furtherance of a claim that would, if meritorious, change the outcome of the case. As in Hartfield and Bass , we cannot say for certain whether the expert services, if provided, would vindicate the defendant’s claim. But such uncertainty was not fatal to the defendants’ respective appeals in those cases, and we therefore conclude that it is not fatal here. Of course, defendants should not be permitted to delay proceedings and sap valuable judicial resources with frivolous allegations of claims or defenses that tend to require expert help to establish. Rodriguez’s fair cross-section claim, however, is far from a shot in the dark: Rodriguez has established two of the three prongs of the Duren prima facie case and alleged a plausible theory in support of the third. We hold that, under the circumstances, it was an abuse of discretion not to grant him the expert help he requested to try to make out his fair cross-section claim.

We express no opinion as to the likelihood that Rodriguez’s fair cross-section claim will ultimately succeed, as we do not know what a study of the matter will reveal. We therefore decline currently to vacate Rodriguez’s conviction. We reverse only the denial of his motion to have an expert appointed, and we remand for further proceedings. Once the expert has done his or her work, the district court will be in a position to reassess Rodriguez’s underlying motion to dismiss the indictment. If Rodriguez establishes the prima facie case, the burden will shift to the government in accordance with Duren . If, at that point, the government cannot carry its burden, then the district court must grant Rodriguez’s motion to dismiss the indictment and set aside the conviction.

B. Application of Sentencing Guidelines on Acceptance of Responsibility

A district court’s application of the federal Sentencing Guidelines is reviewed de novo. United States v. Nielsen, 371 F.3d 574, 582 (9th Cir.2004).

Rodriguez argues that he was entitled to an additional one-level reduction in his sentencing range because of his acceptance of responsibility. The Guidelines provide for a two-level reduction for acceptance of responsibility, see U.S. Sentencing Guidelines Manual § 3El.l(a) (2002), and an additional one-level reduction for defendants at level 16 or greater where the defendant has assisted authorities by “(1) timely providing complete information to the government concerning his own involvement in the offense,” or “(2) timely notifying authorities of his intention to enter a plea of guilty,” or both, id. § 3El.l(b).

A district court commits reversible error if it fails to apply the additional one-level reduction where the defendant has satisfied either subsection of U.S.S.G. § 3El.l(b). United States v. Ruelas-Arreguin, 219 F.3d 1056, 1062 (9th Cir.2000). In applying these Guideline provisions, “a judge cannot rely upon the fact that a defendant refuses to plead guilty and insists on his right to trial as the basis for denying an acceptance of responsibility adjustment.” United States v. Ochoa-Gaytan, 265 F.3d 837, 842 (9th Cir.2001).

This case is unusual. Before the initiation of his prosecution, Rodriguez told an immigration officer that he was a citizen of Mexico, that he had previously been deported from the United States, and that he did not have official permission to return here. Rodriguez thus admitted all the elements of a violation of 8 U.S.C. § 1326 , the crime for which he was convicted. See Ninth Circuit Model Criminal Jury Instructions 9.5 (2003). Nonetheless, Rodriguez exercised his right to require the government to carry its burden to prove his guilt. At sentencing, the district court gave a two-level reduction for acceptance, but declined to give a third level “because we went to trial, and we didn’t have [the acceptance of responsibility] timely.” Despite the district court’s statement to Rodriguez that the court was “not going to hold it against you in any way [that] you went to trial,” this is exactly what the court did.

Because Rodriguez “timely provided] complete information to the government concerning his own involvement in the offense,” U.S. Sentencing Guidelines Manual § 3El.l(b)(l) (2002), he was entitled to the additional one-level reduction for acceptance of responsibility. Ruelas-Arreguin, 219 F.3d at 1062 . The district court erred in not granting that reduction and in penalizing Rodriguez for going to trial. The government concedes as much.

Because Rodriguez did not object at sentencing, the panel must review for plain error, which is “(1) error, (2) that is plain, and (3) that affects substantial rights.” United States v. Ameline, 409 F.3d 1073, 1078 (9th Cir.2005) (en banc) (citation and internal quotation marks omitted). “If these three conditions of the plain error test are met, an appellate court may exer cise its discretion to notice a forfeited error that (4) seriously affects the fairness, integrity, or public reputation of judicial proceedings.” Id. (citation and internal quotation marks omitted).

As we have explained, the district court erred when it gave Rodriguez two levels instead of three for acceptance of responsibility. The district court’s error was plain, because it is contrary to the law at the time of Rodriguez’s appeal. Id. (citation and internal quotation marks omitted). We also conclude that Rodriguez’s substantial rights were affected: because he was entitled to a lower Guideline range than that under which he was actually sentenced, the outcome of Rodriguez’s sentencing was affected such that our confidence in that outcome is undermined. Cf. Glover v. United States, 531 U.S. 198, 202-04 , 121 S.Ct. 696 , 148 L.Ed.2d 604 (2001) (holding, in the ineffective-assistance-of-counsel context, that any increase in a defendant’s sentence is prejudicial); United States v. Dominguez Benitez, 542 U.S. 74 , 124 S.Ct. 2333, 2339-40 , 159 L.Ed.2d 157 (2004) (likening the plain-error “substantial rights” inquiry to the prejudice standard applicable to, among other things, claims of ineffective assistance of counsel).

Finally, we conclude that the error seriously affected the fairness, integrity, or public reputation of the proceedings, because the district court penalized Rodriguez for exercising his constitutional right to go to trial. The unfairness of penalizing a defendant for exercising his legal rights has long been recognized in our national jurisprudence and needs no elaboration. See, e.g., North Carolina v. Pearce, 395 U.S. 711, 724 , 89 S.Ct. 2072 , 23 L.Ed.2d 656 (1969); Griffin v. California, 380 U.S. 609, 614-15 , 85 S.Ct. 1229 , 14 L.Ed.2d 106 (1965). It is equally clear that public confidence in the justice system is jeopardized by any such practice, in which basic rights are undercut by the very institution charged with their protection. Cf. Olmstead v. United States, 277 U.S. 438, 485 , 48 S.Ct. 564 , 72 L.Ed. 944 (1928) (Brandéis, J., dissenting) (“Our government is the potent, the omnipresent teacher. For good or for ill, it teaches the whole people by its example.”) We therefore have no difficulty concluding that the sentencing error in Rodriguez’s case, though a small one, seriously affected the fairness, integrity, or public reputation of the judicial proceeding.

We hold that the district court’s’ failure to give the third level of the aceeptance-of-responsibility reduction was plain error. Rodriguez’s sentence must be vacated.

C. Prior Convictions and Apprendi

Rodriguez also claims his sentence is unconstitutional under Apprendi v. New Jersey, 530 U.S. 466 , 120 S.Ct. 2348 , 147 L.Ed.2d 435 (2000), and its progeny, because the fact of his prior conviction for transport of methamphetamine, which resulted in a 16-level enhancement of Rodriguez’s sentencing range, was not admitted by Rodriguez or proved to a jury beyond a reasonable doubt. Rodriguez’s argument is foreclosed by United States v. Smith, 390 F.3d 661 (9th Cir.2004), which held that Blakely v. Washington, 542 U.S. 296 , 124 S.Ct. 2531 , 159 L.Ed.2d 403 (2004), did not disturb the “prior conviction” exception to the Apprendi rule. See Smith, 390 F.3d at 667 . This understanding was confirmed in Booker, which repeated the “pri- or conviction” exception in its rendition of the Apprendi rule. See 125 S.Ct. at 756. Finally, Shepard v. United States, — U.S. -, 125 S.Ct. 1254 , 161 L.Ed.2d 205 (2005), does not counsel a different result, as the district court in this case did not need to resolve a “disputed fact ... too far removed from the conclusive significance of a prior judicial record.” Id. at 1262 (plurality portion). In this case, Rodriguez’s enhancement was supported by the abstract of judgment and charging document for the prior conviction.

CONCLUSION

The issue of jury representativeness is one that goes to the heart of one of our nation’s fundamental judicial institutions. “For racial discrimination to result in the exclusion from jury service of otherwise qualified groups not only violates our Constitution and the laws enacted under it but is at war with our basic concepts of a democratic society and a representative government.” Smith v. Texas, 311 U.S. 128, 130 , 61 S.Ct. 164 , 85 L.Ed. 84 (1940) (footnote omitted). If our system of jury selection results in the systematic exclusion of a distinctive group, we have a responsibility to discover the problem and remedy it. As a matter of basic fairness, our Constitution promises individuals charged with crimes that their juries will represent a fair cross-section of the community. Rodriguez raises a serious claim that the our system is not keeping that promise; without further study, we cannot know for sure that he is wrong.

We hold that the district court abused its discretion in denying Rodriguez’s motion to have an expert appointed, and that the district court committed plain error by giving a two-level rather than a three-level reduction for Rodriguez’s acceptance of responsibility.

We therefore reverse the district court’s denial of Rodriguez’s motion to have an expert appointed, vacate Rodriguez’s sentence, and remand for further proceedings consistent with this opinion, including re-sentencing, the appointment of an expert, and the subsequent reconsideration of Rodriguez’s motion to dismiss the indictment.

REVERSED AND SENTENCE VACATED. REMANDED;

APPENDIX: CALCULATION OF ABSOLUTE DISPARITY FOR HISPANIC REPRESENTATION IN FRESNO DIVISION JURY POOL

Age-eligible population for the eleven Fresno Division counties (2000 Census):

Total Population, age 18 + Hispanic Population, age 18 +

Fresno 542,982 214,927

Tulare 243,769 109,083

Merced 137,870 55,884

Kings 91,933 736,259

Kern Madera 450,266 86,642 150,738 33,164

Stanislaus 307,775 83,599

Inyo 13,569 1,338

Tuolumne 43,201 3,319

Mariposa 13,427 945

Calaveras 31,306 1,769 Percent

Fresno Division Hispanic: Total 1,962,740 691,025 35.21%

Representation in the 2003 Qualified Jury Wheel:

Total Percent Percent of those of Total reporting

Hispanic 971 15.77% 20.66%

Non-Hispanie 3728 60.54% 79.34%

Unknown 1459 23.69% —

Total 6158 100% —

Total reporting ethnicity 4699 776.31% 100%

Percent Hispanic of 18 + Population 35.21

- Percent Hispanic in Jury Pool - 20.66

= Absolute Disparity = 14.55%

. We take judicial notice of the Eastern District’s most current juror selection plan, which replaced the 1992 plan included in the record. We note that the feature of the plan most salient to Rodriguez’s claims remains unchanged: the 1992 plan, like the current plan, calls for the use of voter registration records as the sole source of names for the master jury wheel. . Although Rodriguez styled his equal protection claim as one arising under the Fourteenth Amendment, a claim of discrimination by the federal government implicates the equivalent equal protection guarantee inherent in the Due Process Clause of the Fifth Amendment. See Bolling v. Sharpe, 347 U.S. 497 , 74 S.Ct. 693 , 98 L.Ed. 884 (1954). In accordance with our duty to construe pro se motions and pleadings liberally, see, e.g., Bernhardt v. Los Angeles County, 339 F.3d 920, 925 (9th Cir.2003), we treat Rodriguez's equal protection claim as one under the Fifth Amendment. Rodriguez also alleged a violation of the JSSA, but we need not consider this claim independently, because "[t]he test for a constitutionally selected jury is the same whether challenged under the Sixth Amendment of the Constitution or under the Jury Selection and Service Act.” United States v. Sanchez-Lopez, 879 F.2d 541, 546 (9th Cir.1989) (citation and internal quotation marks omitted). . Rodriguez alleged an "absolute disparity” of 37.4%, a figure that is not borne out by the data. As we shall explain, the data do reflect substantial underrepresentation of Hispanics, just not to the extent Rodriguez claims. . The court mischaracterized the government’s data. For the state assembly district in question, the 17% figure represented the proportion of the registered-voter population that was Hispanic, not the proportion of the jury-eligible population that was Hispanic. . The Ninth Circuit case to which the court referred, United States v. Jones, was an unpublished memorandum disposition. 91 F.3d 156 (9th Cir.1996). The district court case, United States v. Luong, rejected a challenge to jury composition in the Sacramento Division, not the Fresno Division, of the Eastern District. 255 F.Supp.2d 1123, 1126, 1131 (E.D.Cal.2003). . The following day, on the morning of trial, the court indicated it was supplementing the record of the denial of Rodriguez's motion with additional statistics provided by the government The relevance of these statistics, which reflect demographics for the total population and the registered voter population of State Board of Equalization District Two, is unclear. The Fresno Division includes 11 counties. State Board of Equalization District Two includes 31 entire counties and portions of 3 others. Some counties partially included in District Two, such as San Bernar-dino and Los Angeles, are not even part of the federal Eastern District, much less the Fresno Division. . Judge Kleinfeld concurred only in the result; Judge Boochever, in a “concurrence and partial dissent,” would have preferred to remand to the district court instead of taking judicial notice of the data reflecting the age-eligible population. See id. at 728-29. . Prior to Artero , one other Ninth Circuit case suggested, without discussion or citation, that the appropriate comparison group for the second Duren prong is the "number of eligible minorities.” United States v. Cannady, 54 F.3d 544, 548 (9th Cir.1995). The decision did not elaborate on this proposition or clarify whether it was referring to age-eligible or juiy-eligible minorities. . While its precedential pedigree and fidelity to Supreme Court jurisprudence are what compel us to follow the view reflected in Sanchez-Lopez and Esquivel , our conclusion is fortified by the evident wisdom of this position on its merits. Whereas census data are readily accessible, jury-eligible population data will often be quite hard for fair-cross-section claimants to obtain, given the difficulty of sorting out from the general population figures the number of individuals who (for example) are not citizens, who are not fluent in English, or who are “incapable, by reason of mental or physical infirmity, to render satisfactory jury service.” 28 U.S.C. § 1865 (b) (federal jury qualifications). Other courts have noted the potentially "insuperable” burden that requiring such data could place on fair-cross-section claimants, United States v. Butera, 420 F.2d 564 , 569 n. 13 (1st Cir.1970), overruled on other grounds, Barber v. Ponte, 772 F.2d 982, 996 (1st Cir.1985) (en banc), as well as scholars’ conclusion that "eligible population figures are almost impossible to obtain.” People v. Harris, 36 Cal.3d 36 , 201 Cal.Rptr. 782 , 679 P.2d 433, 442 (1984) (plurality opinion) (quoting David Kairys et al., Jury Representativeness: A Mandate for Multiple Source Lists, 65 Cal. L.Rev. 776, 785 n.63 (1977) (internal quotation marks omitted)), not followed on other grounds, People v. Sanders, 51 Cal.3d 471 , 273 Cal.Rptr. 537 , 797 P.2d 561, 570-72 (1990); see also Hon. Walter P. Gew-in, An Analysis of Jury Selection Decisions, Appendix to Foster v. Sparks, 506 F.2d 805, 811, 833 (5th Cir.1975). Requiring a fair-cross-section claimant to come forward with a comparison to the jury-eligible population thus risks placing one of the elements of the prima facie case for equal protection and fair cross-section claims out of reach, thereby insulating jury selection systems from judicial scrutiny entirely. So it stands to reason that none of the Supreme Court's cases has charged a fair-cross-section claimant with the affirmative obligation to compile data reflecting the jury-eligible population. In fact, we have found no case, before or after Duren , in which the Supreme Court rejected a prima facie showing of underrepresentation because of a failure to provide statistics reflecting the distinctive group’s proportion in the juiy-eligible— as opposed to the general or age-eligible— population. To reiterate the Supreme Court's admonition in Duren , "the fair-cross-section requirement involves a comparison of the makeup of jury venires or other sources from which jurors are drawn with the makeup of the community." 439 U.S. at 365 n. 23, 99 S.Ct. 664 (emphasis in original). . The main alternative measure of representativeness is "comparative disparity,” which is determined by taking the absolute disparity percentage and dividing it by the percentage of the distinctive group in the total popula tion. See Sanchez-Lopez, 879 F.2d at 548 . For example, if Hispanics are 20% of the community and 5% of the jury pool, the absolute disparity is 15% (20% minus 5%), and the comparative disparity is 75% (15% divided by 20%). Each measure has its limitations. The comparative disparity method can distort the effect of disparities in representation when absolute numbers are low. See, e.g., Armstrong, 621 F.2d at 955-56 . For example, if Hispanics are 2% of the community and 1% of the jury pool, the comparative disparity is 50%, but for every 100 jurors, there is only one fewer Hispanic than would be proportional. However, absolute disparity is also problematic. For example, our circuit has tolerated absolute disparities in distinctive group representation of up to 7.7%. See Suttiswad, 696 F.2d at 649 . The necessary implication of this margin is that if a distinctive group makes up 7.7% or less of the community, then the fair cross-section requirement offers no redress even if that group is entirely shut out of the jury pool. See Kairys et ah, 65 Cal. L.Rev. at 793 ("[I]n the 11% black jurisdiction, the 10% absolute disparity amounts to almost total exclusion of black people.”). While Ninth Circuit precedent requires us to evaluate representativeness using absolute disparity statistics alone, that approach is not without short-comings. . Our calculations are set out in an Appendix to this opinion. Two points should be noted. First, we use the age-eligible population figures that are available in the record. See Esquivel, 88 F.3d at 726-27 (opinion of T.G. Nelson, J., announcing the judgment of the panel). Second, to address the problem of the 24% of the qualified jury wheel whose ethnicity was unreported, the ethnicity percentages were recalculated as a percentage of the jurors whose ethnicity was reported. In other words, to avoid distorting the numbers by using the percentage of reported Hispanics as a percentage of all prospective jurors including those not reporting their ethnicity (an approach that would unrealistically assume that none of the jurors not reporting their ethnicity were Hispanic), the individuals not reporting were simply not included in the percentage calculations. Therefore the calculations reflect no assumptions about the ethnicity of those not reporting. . The district court rejected Rodriguez's claim in part based on the judge’s personal observations about the representativeness of the juries he has seen. The case law provides no support for taking such observations into account under Duren . . In People v. Sanders, the California Supreme Court refused to read Harris as standing for the proposition that “sole reliance on voter registration lists in assembling the master jury list is constitutionally prohibited.” 273 Cal.Rptr. 537 , 797 P.2d at 570-71 . The court distinguished Harris on the ground that the court's understanding of the prima facie case for a fair cross-section violation had changed since that decision; under the California Supreme Court's new interpretation, a defendant had to demonstrate that selection procedures were themselves constitutionally impermissible or being applied in a constitutionally objectionable manner. Id. at 571-72. As the California Supreme Court's revised understanding of the prima facie case under Duren is not a view our circuit has shared, the Harris plurality's recognition of the exclusionary effect of the use of voter registration lists as the sole source for jury pools retains some persuasive value for us in the following limited sense: Harris suggests that Rodriguez's theory about the effect of sole reliance on voter registration lists is quite plausible rather than fanciful. It bears noting that challenges to the use of voter registration lists as the sole source for jury pools have not met with success in the federal courts. See generally United States v. Cecil, 836 F.2d 1431, 1445-49 (4th Cir.1988) (en banc) (collecting cases and discussing the history of such challenges in the courts). However, defendants' failure to support such challenges in the past does not preclude the possibility that Rodriguez may do so here. For the purposes of this case, the important point is that there is some empirical and legal support for Rodriguez's theory, even if it has not generally been a successful one. . In the published cases involving the denial of an expert in this context, panels have denied relief based on the defendant's failure to show that reasonably competent counsel would have required the services of an expert, not on the basis of a failure to demonstrate prejudice. See Nelson, 137 F.3d at 1101 n. 2; Suttiswad, 696 F.2d at 649 ; Armstrong, 621 F.2d at 956 . . Because our analysis of the fair cross-section claim has led us to conclude that the district court should have appointed an expert, we need not consider whether Rodriguez’s showing on his equal protection claim also entitled him to the requested expert. . Our substantial rights analysis is unaffected by the advisory nature of the Sentencing Guidelines in the wake of United States v. Booker, - U.S. -, 125 S.Ct. 738 , 160 L.Ed.2d 621 (2005), for we have held that a pre-Boo/cer misapplication of the Guidelines still requires that the resulting sentence be vacated, notwithstanding the transformations in sentencing law wrought by Booker. See Ameline, 409 F.3d at 1085-86 ; United States v. Kimbrew, 406 F.3d 1149, 1154 (9th Cir.2005).