This case raises two trial issues: (1) the instructions on “beyond a reasonable doubt” and on lost evidence, and (2) ethnic composition of the grand jury.
I. FACTS
Artero was convicted of smuggling marijuana across the Tijuana-San Diego border in his gas tank (importation in violation of 21 U.S.C. §§ 952 and 960, and possession with intent to distribute in violation of 21 U.S.C. § 841(a)(1)).
Artero was driving into the United States from Mexico. The initial inspector at U.S. Customs thought the car was too clean and lacking in personal effects, so he directed Artero to a secondary inspection. When the inspectors had Artero open the trunk, they saw a full plastic gasoline container, which was very unusual. The inspector asked why, and Artero’s answer, that the gas in Mexico was bad, seemed strange. So the inspector looked at the gas tank under the car, which also looked too clean, cleaner than the rest of the underside of the ear. The narcotics dog scratched at the back of the car, and the gas tank sounded solid instead of hollow. An inspector tried to drive the car to the service station where they routinely remove gas tanks, but it ran out of gas, though the gas gauge was past the full mark. When they got the gas tank off the car and took it apart, • specially packaged marijuana filled almost all the space that was designed to hold gasoline.
II. ANALYSIS
Artero raises three points on appeal, the “beyond a reasonable doubt” instruction, denial of an instruction inviting the jury to draw a negative inference from the government’s loss of the one gallon gas can, and the composition of the grand jury.
A. Jury Instructions.
1. “Beymd a Reasonable Doubt” Instruction.
The trial judge used a modified version of the Federal Judicial Center form book instruction for “beyond a reasonable doubt.” Here is the instruction as given, underlined to show the parts we discuss:
Proof beyond a reasonable doubt is proof that leaves you firmly convinced of the defendant’s guilt. There are very few things in this world that we know with *1258absolute certainty, and in criminal cases the law does not require proof that overcomes every possible doubt. If you are firmly convinced that the defendant is guilty, you must find him guilty.
But if you think there’s a real possibility that the defendant is not guilty, you must give him the benefit of the doubt and find him not guilty. You may not convict on the basis of mere suspicion.
(Emphasis added). Except for the last sentence, which Artero does not attack, this instruction is substantially copied from the Federal Judicial Center form book. Federal Judicial Center, Pattern Criminal Jury Instructions 28 (1988) (instruction 21).
Artero’s argument is directed at the phrase “real possibility” in the sentence, “But if you think there’s a real possibility that the defendant is not guilty, you must give him the benefit of the doubt and find him not guilty.” He says “real possibility” is more than “reasonable doubt,” and also that the phrasing implies that it is the defendant’s burden to establish the “real possibility.”
We have already concluded that “real possibility” is permissible in United States v. Bustillo, 789 F.2d 1364, 1368 (9th Cir.1986). This case differs only in that there was an objection in the district court, while in Bustillo we reviewed for plain error. We see no reason to limit Bustillo to plain error. We explained in United States v. Newport, 747 F.2d 1307 (9th Cir.1984), that “the term ‘real’ means a doubt which is [ ] authentic, genuine, actual and true instead of its opposite meaning i.e. ‘unreal, apparent, or imaginary’ doubt.” Id. at 1308. The Supreme Court has held that a reasonable doubt is, at a minimum, one based on reason, so “[a] fanciful doubt is not a reasonable doubt.” Victor v. Nebraska, 511 U.S. 1, 17, 114 S.Ct. 1239, 1248, 127 L.Ed.2d 583 (1994). Victor makes that distinction in the context of approving the phrase “not a mere possible doubt.” Id.
“[T]he Constitution does not require that any particular form of words be used in advising the jury of the government’s burden of proof.” Id. at 5, 114 S.Ct. at 1243. The Federal Judicial Center form book instruction used for the challenged passage is the one recommended by Justice Ginsburg in her concurrence in Victor. Id. at 26-27, 114 S.Ct. at 1253-54 (Ginsburg, J., concurring). The trial judge may require a “real possibility” of doubt because “[a] fanciful doubt is not a reasonable doubt.” Id. at 17, 114 S.Ct. at 1248. The phrase “real doubt” does not suffer the infirmity of requiring the jury to have “grave uncertainty,” “substantial doubt,” and a “real tangible substantial basis” for doubt, before they can acquit, as the unconstitutional instruction did in Cage v. Louisiana, 498 U.S. 39, 40, 111 S.Ct. 328, 329, 112 L.Ed.2d 339 (1990), overruled on other grounds by Estelle v. McGuire, 502 U.S. 62, 72 n. 4, 112 S.Ct. 475, 482 n. 4, 116 L.Ed.2d 385 (1991).
The Federal Judicial Center form has the virtue of using the common phrase “give him the benefit of the doubt.” Most jurors are likely to have spoken that way themselves, when they mean “I think something is probably true, but I’m not sure, so I’ll give him the benefit of the doubt.” That is the right way for the jurors to interpret “beyond a reasonable doubt” — not just whether they think the defendant more likely than not committed the crime charged, or even that he most probably did, but whether they are sure that he did, and if not, he should get the benefit of what is merely a doubt and not a probability. The “real possibility” phrase, in the context of the whole instruction, does not put a thumb on the scales as the Cage instruction did, telling the jury that it could not acquit unless the doubt rose to “grave uncertainty,” “substantial doubt,” and a “real tangible substantial basis.” One can imagine reasonable jurors in Cage saying, erroneously, “I’m not sure he did it, but I don’t have a real tangible substantial basis for that — it’s just that the evidence leaves open a real possibility that he didn’t do it, so I have to convict because I can’t identify a real tangible substantial basis for my doubt.” By contrast, under the Federal Judicial Center form book instruction used here, that juror would be led to say, correctly, “So I have to give him the benefit of the doubt, even though he probably did it.” We do not consider whether the language “you may not convict on ... mere suspicion,” implies that anything more than mere suspicion, such as probable cause or preponder*1259anee of evidence, will suffice, because Artero has not put that sentence at issue.
2. Denial of Adverse Inference Instructions.
At trial, the government was unable to introduce the gas can that Customs had found in Artero’s trunk. Government personnel had lost the gas can. The government put into evidence the car’s gas tank, or what it claimed was the car’s gas tank, but the chain of custody was poorly established. Artero asked for a jury instruction that “you may infer” from the government’s failure to introduce the gas can as evidence “that the container never existed.” He also asked for an instruction telling the jury that “you are not required to believe that the gas tank placed in evidence is the one recovered from Mi-. Artero’s automobile,” and that “you may consider whether its characteristics are the ones the government claims it had on the night the ear was seized.”
The gas can from the trunk was important to scienter. Artero could have innocently driven a car with its gas tank full of marijuana, if he were a “blind mule.” A blind mule is a person used by criminals to carry contraband across a border, who does not know that he is carrying the contraband. A driver is less likely to be unaware of the existence of a can of gasoline in his trunk than an altered gas tank — all of us look in the trunk much more often than we look at the undersides of our ears, and a full gas can usually smells. The gas can in the trunk substantially reduced the likelihood that the jury might doubt scienter.
Evidence on the gas can was so weak that reasonable jurors might have inferred, as defense counsel argued, that the gas can never existed. Inspector David Morris, who had picked out Artero’s car as suspicious and noticed that his gas tank was cleaner than the rest of the undercarriage, said there was a small red plastic gas can, probably 1.1 gallons, in the trunk, emitting a strong odor of gasoline when he opened the trunk. Inspector Robert Schulze drove the car (and had it pushed when it ran out of gas) to the service station, had the gas tank removed, and saw the marijuana packages inside it where gasoline should have been. He saw the gas can in the trunk too, but he guessed it was a two or three gallon container. Special Agent Susan Aarons, the case agent called in to take custody of the evidence, arrest the defendant, and help prosecute the case, testified that the gas tank was placed in a hallway, and that she mistakenly did not see that it was put back into the vehicle until a couple of months afterward, when she retrieved it from the Port of Entry in San Ysidro. She had written in her report that Inspector Morris had told her there was a full five gallon gasoline container, but when she photographed the trunk of the car, the gas can was not in the trunk. Although she photographed the car, the gas tank, and the marijuana, she did not photograph the gas can. She testified that she would not have seized and stored the gas can because she would have considered it hazardous to herself.
Artero cites no authority for the proposition that the court was obligated to instruct the jury that it could draw inferences against the prosecution from these evidentiary gaps. He cites United States v. Tory, 52 F.3d 207, 211 (9th Cir.1995), but all that held was that the “defense should have been allowed to argue” for an adverse inference. In the case at bar, the judge expressly provided that the defense counsel could argue for adverse inferences, which is all that Tory might require.
In United States v. Jennell, 749 F.2d 1302, 1308-09 (9th Cir.1984), we held that the district judge did not abuse his discretion by refusing to give an adverse inference instruction, because the appellant showed neither bad faith imputable to the federal government nor prejudice from the loss and destruction of the evidence. The case at bar cannot reasonably be distinguished.
There is no reason to suppose that the government destroyed the gas can and did not photograph it in bad faith, that is, to hide it from the defense or prevent the jury from seeing what it looked like. That would make no sense, because preservation could only help the prosecution, and loss could only help the defense. Even if it were a ten gallon green metal can, instead of a one, three, or *1260five gallon red plastic can, preserving it and putting it before the jury would prove that it existed, and support the inference of scienter. That it would impeach the recollections of all three witnesses who had testified to what it looked like could not have mattered much, because they impeached each other anyway, and what mattered was merely whether Artero had a container of gasoline in his trunk. The loss of the gas can facilitated a plausible argument that the gas can never existed. Likewise, the defense was free to argue as its requested instruction would have suggested, that the sloppy chain of custody evidence on the gas tank left open the possibility that the jury had been shown the wrong gas tank, one not from Artero’s vehicle. It was also free to argue, as it did, that the government’s success in finding the lost gas tank made it likely that the government would have found the gas can too, had it really existed, so it probably did not. We are unable to figure out how bad faith could be attributed to the government in this particular evidentiary mess, or how the loss of the gas can or temporary loss of the gas tank could have prejudiced the defense.
B. Composition of the Grand Jury.
Artero argues that the grand jury that indicted him was not a fair cross section of the population, because it underrepresented persons of Hispanic ethnicity. He was indicted in the Southern District of California. He presented declarations claiming that 24.2 percent of the population in the district, but only 9.7 percent of the people in the jury wheel, were Hispanic, a 14.5% disparity.
“It is the policy of the United States that all litigants in Federal courts entitled to a trial by jury shall have the right to grand and petit juries selected at random from a fair cross section of the community in the district or division wherein the court convenes.” 28 U.S.C. § 1861. Artero was constitutionally entitled to a grand jury randomly drawn from a representative cross section. United States v. Esquivel, 88 F.3d 722, 724 (9th Cir.1996). To establish a prima facie case for violation of the fair cross section requirement, a person challenging the venire must show distinctiveness of the group excluded, unreasonable representation of that group, and that the underrepresentation of that group was caused by systematic exclusion:
In order to establish a prima facie violation of the fair-cross-section requirement, the defendant must show (1) that the group alleged to be excluded is a “distinctive” group in the community; (2) 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; and (3) that this underrepresentation is due to systematic exclusion of the group in the jury-selection process.
Duren v. Missouri, 439 U.S. 357, 364, 99 S.Ct. 664, 668, 58 L.Ed.2d 579 (1979).
The government does not dispute the distinctiveness of Hispanics. Artero argues that the numerical disparity is too great to be reasonable, and that using voter registration lists as a basis for the jury wheel amounted to systematic exclusion because fewer Hispanics than non-Hispanics register to vote. The government argues that because a higher percentage of Hispanics than non-Hispanics in the district are probably ineligible to serve on juries, no unreasonableness was demonstrated, nor can use of voter registration lists be deemed systematic exclusion of eligible persons. The Federal Defenders and the United States Attorney in San Diego have fought this same battle in numerous cases, using the same declarations, and the district judges have rejected the challenge for the same reason: that the apparent disparity between Hispanics in the district and those in the jury wheel does “not contemplate the number of those who are not eligible for selection on a jury.” Esquivel, 88 F.3d at 726.
In Esquivel, we affirmed despite the identical challenge to the identical Southern District of California jury wheel based on the identical declarations.1 The only difference between the case at bar and Esquivel is that in that case, the government presented census data during the appeal, of which we took *1261notice, showing that the district judges in the Southern District were right in concluding that the defense expert’s statistics did “not contemplate the number of those who are not eligible for selection on a jury.” Once the category of Hispanics was narrowed down to those Hispanics eligible to serve on juries, the disparity dropped from the defense claim of 14.5% to 4.9%. This reduction in the disparity to 4.9% meant there was no prima facie case, because it was less than the 7.7% disparity held not to be unreasonable in United States v. Suttiswad, 696 F.2d 645, 649 (9th Cir.1982). In Esquivel, we rejected an equal protection challenge, identical to one urged in the case at bar, because there was no showing of discriminatory intent, Esquivel, 88 F.3d at 727-28, and that holding controls the same issue in this case.
There would obviously be a degree of pointlessness about reversing the case at bar based on a 14.5% disparity which we know from Esquivel does not exist. Like Esquivel, we conclude that the defense did not make a prima facie case of underrepresentation. Because we have not been asked in this case to take judicial notice of the census data presented by the government in the Esquivel appeal, we reach the same conclusion for different reasons. The defense statistics did not themselves make out a prima facie case, because the defense expert used the wrong numerator for the ratio of Hispanics to the general population.
To serve on a federal grand jury, a person must be a citizen of the United States, at least 18 years old, and speak English. 28 U.S.C. § 1865(b)(l)-(3). The able district judges in the Southern District were cognizant that the district, consisting of two counties on the border with Mexico, would likely have many Hispanic residents who had not yet attained citizenship or English proficiency, because they had only recently come to the United States to seek better work to support themselves and their families. As a matter of common sense, the percentage of Hispanics eligible for federal jury service in those two counties was likely to be lower than the ratio for the general population.
The question before us is limited to whether that common sense judgment must be reversed because the government did not present rebuttal evidence, or whether the disparity claim in the defense declarations could be rejected on its face. In United States v. Sanchez-Lopez, 879 F.2d 541, 547-48 (9th Cir.1989), where the government also failed to present any evidence, we assumed the validity of the statistics for purposes of discussion. Sanchez-Lopez does not help us resolve this case, though, because we did not hold that such data was valid, or that validity had to be assumed in the absence of rebuttal evidence, and we concluded that there was no prima facie case regardless. Id. at 548.
The defense presented a declaration from John R. Weeks, Ph.D., a demographer. He extrapolated from the 1990 census data showing that San Diego and Imperial Counties were 22.3% Hispanic, that they were probably about 24.2% Hispanic in 1993. Then he applied a Spanish surname search program to the jury wheel, and found that 9.7% of the names were so identified. Dr. Weeks noted that Hispanics are less likely to be registered to vote than non-Hispanics, and so he inferred that the voting registration list would underrepresent them as a proportion of the population.
The right question is whether Hispanics eligible to serve on federal juries were unreasonably underrepresented because of systematic exclusion. See United States v. Cannady, 54 F.3d 544, 548 (9th Cir.1995) (“number of eligible minorities”). But Dr. Weeks did not provide any data responsive to that question. He provided an answer to a different question, whether Hispanics, whether eligible to serve on federal juries or not, were represented in jury wheels at a lower rate than their proportion of the population as a whole. Irrelevant question, irrelevant answer. The degree to which Dr. Weeks’ presentation begged the question is highlighted by his suggestion that the number of Hispanics registered to vote would underrepresent the percentage of Hispanics in the population. If Hispanics in Imperial and San Diego Counties were less likely than others to be citizens, then non-citizenship rather than systematic exclusion of qualified individuals would explain both lower percentages of reg*1262istered voters and lower representation in the jury wheel.
Sometimes a distinctive group’s proportion of the population is an adequate substitute for its proportion of those eligible to serve on federal juries. For example, in Duren, there was no reason to doubt the usefulness of comparing the percentage of women summoned for jury service to the percentage in the district, because there is no reason to think women would be disproportionately ineligible to serve on juries. 439 U.S. at 365-66, 99 S.Ct. at.669-70. Probably a higher percentage of women than men are jury-eligible, because women on average live longer and get convicted of felonies less than men. But in our nation of immigrants, it stands to reason that border counties and ports of entry would have significant numbers of immigrants not yet eligible to serve on federal juries. It took many of our ancestors a while to learn English and become citizens.
One claiming underrepresentation of a distinctive group must, to establish a prima facie case, present data showing that the percentage of persons in that group in the jury wheel is significantly lower than the percentage eligible to serve on juries. In this proposition, we follow the Fifth Circuit holding that a comparison of percentages in the jury wheel and “the gross population” is “irrelevant,” because “the pertinent inquiry is the pool of [the group claimed to be underrepresented] in the district who are eligible to serve as jurors.” United States v. Fike, 82 F.3d 1315, 1321 (5th Cir.1996). Where there is no reason to suppose that the percentage of persons in that group in the population is higher than the percentage eligible to serve, then the former may adequately support an inference as to the latter. Where such an inference is not reasonable, then disparity of percentages in the general population and in the jury wheel cannot suffice, because the general population ratio does not imply the jury-eligible ratio.
An expert witness’s post-graduate degree does not protect the court against the tendentiousness of advocacy research. A judge must exercise independent judgment to “ensure that any and all scientific testimony or evidence is not only relevant, but reliable.” Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579, 589, 113 S.Ct. 2786, 2795, 125 L.Ed.2d 469 (1993). “[A] statistical study that fails to correct for salient explanatory variables, or even to make the most elementary comparisons, has no value as causal explanation and is therefore inadmissible in a federal court.” People Who Care v. Rockford Board of Education, 111 F.3d 528, 537-38 (7th Cir.1997). The district judge properly performed that function in this case.
The central inquiry in a criminal case ought to be whether the defendant committed the crime charged. By diverting the inquiry to another subject, “the focus of the trial, and the attention of the participants therein, are diverted from the ultimate question of guilt or innocence that should be the central concern in a criminal proceeding.” Stone v. Powell, 428 U.S. 465, 489-90, 96 S.Ct. 3037, 3050, 49 L.Ed.2d 1067 (1976). There is a cost to looking for defects in the criminal justice system, during proceedings initiated to determine whether a particular individual committed a particular crime. The cost of looking is not only time and money for the search, but corrosion of public respect for a judicial system that loses its focus on what Stone calls “the ultimate question.” Id.
AFFIRMED.