We review the denial of a writ of habeas corpus. The most substantial issue is whether there was juror misconduct that would entitle the petitioner to a new trial.

Facts

The facts in this case are peculiar, at least to our eyes, to the point of being seriously bizarre. That the facts are bizarre is significant to our analysis.

The victim of the crimes was a young woman who had just moved into an apartment in San Francisco. By the end of the afternoon, the movers had put all her goods into the apartment, including her baby grand piano. Relaxing from the stress of moving, she began playing a classical piece on her piano.

The tenant downstairs from her apartment came upstairs to see her, but not to welcome her. Instead, he complained about the noise. As they were discussing her piano playing, not amicably, the petitioner stepped out of his apartment down the hall from the victim’s and said he would be nailing his apartment door shut.

The music-hater (actually he was not a music-hater — he testified that the music “sounded nice, but it was very loud”) testified that the petitioner said, “Do you mind if I pound this nail in my door?” The victim looked kind of puzzled and said, “No.” The music-hater and the victim exchanged looks and then continued talking about the piano.

After the music-hater’s complaint about the noise, the victim felt deflated about playing the piano, so she went out and got some dinner to bring back to her apartment. As she walked down the hall, the petitioner “was actually nailing his door shut.” He told the victim her piano playing was pretty. She thanked him and invited him to stop by sometime to have tea or coffee. She then ate alone in front of the television, having locked her door with the deadbolt, and went to sleep.

As the victim subsequently discovered, the deadbolt did not work. She had noticed earlier that the doorknob lock did not work, but had no inkling that the deadbolt did not work either. Around two in the morning, she was awakened by the petitioner (the door-nailer) in her apartment. She asked him what he was doing there. He said, as he was “strolling across the living room” toward her bedroom, “he was going to fuck” her. She strongly voiced her refusal, but he said she had “invited” him. She told him “not for this.” He threw her onto her bed. She tried to fight him off, all the while screaming every expletive she could think of. She had no phone yet in her new apartment, so she was hoping her loud voice would rouse a neighbor. He kept telling her that she had invited him, so he had “the right to be there.” He scratched and bruised her face and breasts, ripped the crotch open on her sweatpants, and ripped her shirt, pants, and bra. Then he climbed on top of her and stuck his finger in her anus. She bit him and squeezed his testicles as hard as she could.

Fortunately, the victim’s screaming roused the music-hater. When putting tissue paper in his ears did not suffice to eliminate the noise, the music-hater pounded on the ceiling with a broomstick to tell them to quiet down. At that point, the petitioner got up and walked out. The victim immediately barred her door with a piece of wood and piled-up boxes as well as the ineffectual locks. Meanwhile, the music-hater had put on his overcoat and gone up the fire escape. He did not know she had barred her door, but he explained that going up the fire escape was a shorter distance than going all the way down the hall, up, and all the way back down the other hallway above him. When he got to the victim’s window, he tapped on it to express his desire for quiet.

The victim heard a frightening tapping on her window (not expecting visitors by that route). The music-hater said she turned from where she was piling boxes against her door, and looked at him, “her eyes ... big like flying saucers.” It then occurred to him that she would think he was trying to break in. At first the victim couldn’t tell who it was, and she was “afraid it was going to be more of the same.” She ran over to the window yelling that somebody had tried to rape her, and she found the music-hater, wrapped in an overcoat (he had no pants on), standing on her fire escape. She could tell he was trying to speak to her through the closed window, so she went to another partially opened window to hear what he was saying. He asked what was going on, and she told him the door-nailer had broken into her apartment and tried to rape her. He went around to her door, which she could only open a little, but then he went back to the fire escape out of fear that the door-nailer might see him at the door. Then, deciding that staying on the fire escape was probably “not the gentlemanly thing to do,” he went back to the door and invited her down to his apartment to call the police. They crossed through her apartment and went down the fire escape to use the music-hater’s phone to call the police.

A policeman came to the apartment building in answer to the victim’s call. As he was waiting to be buzzed in, the petitioner walked in with two male transvestite prostitutes, one of whom the police officer had dealt with in the past (the male transvestite prostitutes, he testified, gather a half block away). Rather than arrest the prostitutes, he left them to respond to the more urgent rape call, and found the victim upset, crying hysterically, and very frightened. After talking to the victim, the policeman went to the petitioner’s apartment and arrested him. The rape victim turned down the police officer’s suggestion that she go to the hospital because she did not think she could afford the cost of medical treatment. Later, the victim found the petitioner’s belt in her front entryway.

The petitioner told a very different story at trial. He testified that he was severely injured in a car accident, which put him in a coma, required that a shunt be placed in his brain, and left him with a speech impediment. He met the victim when she and the music-hater were arguing in her doorway. He had broken into his own apartment, wrecking the lock, a week before. After he told the victim he would be nailing his door shut and that he hoped it would not bother her, he told her that the music was wonderful. Later that night, just before midnight, he saw her again when she came into his apartment. She pushed open his broken door, and stared at him lying in his bed, masturbating. Then she invited him back to her apartment to smoke some crack cocaine.

According to the petitioner, he and the victim smoked two or three pieces of crack. Afterward, she asked him to rip her clothes off. He testified that he was bisexual, preferring men, but obliged her (for her pleasure, not his), and obliged her again when she later asked him to insert a finger in her anus. Although she did not explain why she wanted him to do these things, he said his experience had been that people who smoke crack usually like that kind of thing. Then “she started freaking” and bit him, so he left. He testified, “I was still kind of high. I wanted to get somebody I could relate to, and be comfortable with.... [And that’s] a man.” So he left the building to pick up the male transvestite prostitutes.

When recalled to the stand, the victim denied that she had furnished any drugs to the petitioner or taken any herself that day or anytime that week, though she admitted to using speed during previous months. The defense then put on a toxicologist to testify about methamphetamine use and its effects. The prosecutor put on a police officer who testified that the petitioner had told him, “I don’t want to go to prison. I’m sick. I just got out of the St. Mary’s Hospital substance abuse program.”

The jury convicted the petitioner, Gro-temeyer, of first-degree burglary, assault with intent to commit sodomy, sodomy, and false imprisonment. A few weeks after the trial and verdict, one of the jurors contacted the defense lawyer to complain about the jury foreman. The defense moved for a new trial, submitting a declaration from the unhappy juror that the jury foreman, a physician, had improperly used her medical expertise during deliberations. The disgruntled juror made four claims: She alleged that the doctor-foreman (l)“explained that she had ‘been through this before’ and that Mr. Grotem-eyer was indeed guilty of the charges”; (2) said, referring to her medical expertise, that “Mr. Grotemeyer was either mentally ill or retarded, and that his condition caused Mr. Grotemeyer to commit the crime for which he was charged”; (3) “went on to say that ‘an insanity defense should have been mounted’ ”; and (4) “assured me that if the jury voted to convict, Mr. Grotemeyer would receive as part of his sentence, adequate mental health care.” These four statements form the basis for this appeal.

In an amended motion for a new trial, a new lawyer for Grotemeyer submitted a declaration from the music-hater to support an ineffective-assistance-of-counsel claim. The music-hater stated that the victim did not display what would to him seem like the demeanor of a woman who had been raped. He said that while they waited for the police, she asked him to smoke drugs with her and offered him a glass of wine. Later that night, two male friends of the victim arrived, and she hugged one of them, speaking about the incident as if someone had insulted her, not raped her. On another occasion, she told him that she was afraid someone would find out about another incident in Haight-Ashbury in which she had made allegations strikingly similar to this one. He regarded the victim as dishonest because she had not kept her promise to confine her piano playing to the hours she had promised, so it “soon became obvious to me that she was purposely trying to disturb me, and act innocent when confronted about it.” He would have told defense counsel all this, but no one from the defense interviewed him before trial.

The jury foreman submitted a declaration that the Grotemeyer trial was her first jury experience and that she had never told any fellow juror that she had prior jury experience. She further declared that “[njeither during the course of jury deliberations, nor at any other time, did I ever refer to my own medical expertise in offering an opinion about the possibility of petitioner receiving mental health care while in prison.”

The state trial court denied the motion for a new trial without an evidentiary hearing. Grotemeyer appealed, and the California Court of Appeal affirmed. The Court of Appeal analyzed the four alleged statements of the jury foreman under California state law. It held that statements (1) — “been through this before” and Gro-temeyer is guilty — and (3) — “an insanity defense should have been mounted” — were not misconduct. The court thought that “been through this before” could as easily as not refer merely to the ongoing jury deliberations, and that her statement that Grotemeyer was guilty was simply the jury foreman’s opinion based on the evidence. The court held that the statement that an insanity defense should have been mounted was not misconduct.

However, the state appellate court found that statements (2)' — Grotemeyer’s mental illness caused him to commit the crime— and (4) — Grotemeyer would receive adequate mental health care in prison — were misconduct because they were an “injection of external information” into the deliberations. Under California state law, a finding of misconduct triggers a presumption of prejudice. The presumption can be rebutted if the court determines, after a review of the entire record, that it is not substantially likely that the vote of a juror was swayed by the misconduct. The court found the presumption of prejudice to be rebutted because the evidence was “quite strong,” these were “two isolated statements made during nearly ten hours of deliberations,” and the physical evidence supported the victim’s account. The court rejected the argument that the jury foreman was biased because her comments suggested prejudgment of the case or that she swayed jurors based on her medical expertise. The Supreme Court of California summarily denied Grotemeyer’s petition for review. Grotemeyer petitioned in the United States District Court for a writ of habeas corpus, which was denied. He appeals the district court’s denial.

Analysis

Under the Sixth Amendment, Grotemeyer has the right to be tried by an impartial jury and to confront and cross-examine witnesses who testify against him. Moreover, under Turner v. Louisi ana, Grotemeyer is entitled to a jury that reaches a verdict on the basis of evidence-produced at trial, exclusive of “extrinsic evidence.” “In the constitutional sense, trial by jury in a criminal case necessarily implies at the very least that the ‘evidence developed’ against a defendant shall come from the witness stand in a public courtroom where there is full judicial protection of the defendant’s right of confrontation, of cross-examination, and of counsel.”

Grotemeyer makes two principal attacks on the denial of the writ of habeas corpus, both based on the jury foreman’s remarks discussed above. The attacks are (1) that her remarks constituted prejudicial jury misconduct and (2) that the remarks evidenced actual bias. Analytically, these attacks are distinct, and the requirements as to prejudice are different.

The differences do not matter to this case, though, because both analyses depend on there being something wrong, as a matter of federal constitutional law, with the foreman’s remarks. There is not. There was no jury misconduct in the federal constitutional sense, nor was there any showing of denial of an impartial jury.

Much of Grotemeyer’s argument is based- on state law, since the. California Court of Appeal held that, under state law, the jury foreman committed misconduct in two remarks she made. None of that has any relevance to us. A federal court of appeals considering a petition for a writ of heabeas corpus does not review state court decisions pursuant to state law like a state appéllate court. We have authority to grant the writ if and only if the last reasoned state court- opinion “resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.” Thus we look not for a California decision that treats certain remarks made by jurors during deliberations as juror misconduct, but for a United States Supreme Court decision to that effect.

Grotemeyer has not cited one.- His cited authority all goes to extrinsic evidence being introduced into the jury room. That is-altogether different-from a juror sharing her own experiences with her colleagues on the jury. Grotemeyer relies on Parker v. Gladden, but that case does not involve a juror’s remark to her fellows. Rather it concerns a bailiffs remarks to jurors. The other Supreme Court decisions Grotemeyer cites are irrelevant, standing for such general propositions as that a defendant is entitled to confront witnesses and to proof beyond a reasonable doubt. They do not speak to jury misconduct or partiality.

In this case, the charges of juror misconduct and bias arise out of the four alleged remarks by the foreman: (1) that she had “been through this before” and that Grotemeyer was guilty; (2) that she referred to her medical expertise in concluding that Grotemeyer was mentally disturbed and that his condition caused him to commit the crime; (3) that an insanity defense should have been mounted; and (4)that if convicted Grotemeyer would receive, as part of his sentence, adequate mental health care.

Some of the accusations of misconduct are trivial. Like the California Court of Appeal, we do not know just what the allegation about having “been through this before” meant, but it could as easily as anything else have meant that the foreman felt people were repeating themselves as deliberations droned on. The accusation that the jury foreman said she thought Grotemeyer was mentally ill is likewise trivial. Probably most people would think that a person who was nailing his own apartment door shut was mentally disordered, especially when he himself testified that he was brain damaged from a car accident. There was nothing extrinsic to the evidence in the suggestion that he was mentally ill. Nor do we suggest that, were a juror to express such a view without this evidence, it would be misconduct. Jurors are entitled to form opinions about the witnesses and parties before them.

The more substantial extrinsic evidence issues are that the jury foreman, referring to her experience as a medical doctor, opined that Grotemeyer’s mental disorders caused him to commit his crime, and that he would receive treatment as part of a sentence. This raises two subis-sues: what the jury foreman said, and whether she could introduce her medical experience as a basis for saying it.

As to these issues, Grotemeyer has cited no Supreme Court case, and we have found none, holding that such conduct amounts to a violation of his right of confrontation, of his right to an impartial jury, or of any other constitutional right. It is, of course, well established law that a juror may not bring into the jury room evidence developed outside the witness stand such as the results of a juror’s experiment conducted while the jury was on a weekend recess, or legal research performed during the trial in an attempt to supplement inadequate instructions from the judge. But what the jury foreman did here, assuming that she should not have, did not rise to the level of these constitutional violations.

The mere fact that the jury foreman brought her outside experience to bear on the case is not sufficient to make her alleged statements violate Grotemeyer’s constitutional right to confrontation. Counsel ordinarily learn during voir dire what a veniremember does for a living, and use peremptory challenges to avoid jurors whose experience would give them excessive influence. Dr. Papadakis’s expe rience was not shared by the entire jury— it would be extraordinary to have a jury of twelve physicians — but there is nothing wrong with her using it. Juries have long been instructed, in state and federal courts, to do precisely what the foreman did. Usually the boilerplate . instruction reads something like, “You are to base your verdict only on the evidence received in the case. In your consideration of the evidence received, however, you are not limited to the bald statements of the witnesses or to the bald assertions in the exhibits.... You are. permitted to draw from the facts which you find have been proved such reasonable inferences as you feel are justified in the light of your experience and common sense.” We have said in obiter dicta, and now hold, that “a juror’s past personal experiences may be an appropriate part of the jury’s deliberations.” “Indeed, ’50% of the jurors’ time [is] spent discussing personal experiences,’ ” according to one researcher.

The Sixth Amendment entitles a defendant to an “impartial” jury, not to an ignorant one. That a physician is on the jury does not deprive a defendant of his constitutional right to an impartial jury, even though the physician will doubtless have knowledge and experience bearing on any medical questions that may arise. Many trials, including this one, boil down to a question of who is lying. It is hard to know who is lying without some understanding, based on past personal experience, of the circumstances of the witnesses. For example, Wigmore cites a case that a prosecutor lost because his witness testified that a “ready-made pine door” cost ten dollars. ■ As the foreman of the jury — a carpenter by trade — explained, “ Well, he said ten dollars — and I knew he was a liar. A door like that don’t cost but four-fifty!’ ” Often, jurors identify lies by comparing the testimony, to the extent it deals with the familiar, with what they already know to be true.

Evaluation of credibility necessarily relies on experience. Even perfectly plausible allegations can be disbelieved if they occur during the course of a generally impláusible account. If the statement, “I saw a woman milking a cow” (a plausible allegation) comes as part of the account, “I saw a woman milking a cow and the woman and the cow were inside a horse’s head, and there was another woman who was walking upside down on the roof of an upside down house,” the jury is not required to parse the account and believe the cow-milking státement just because it is plausible: When a witness’s account is as unlikely as the events portrayed in a Marc Chagall painting, the jury is entitled to reject the testimony in its entirety, disbelieving both the reasonable and the unreasonable aspects. This, too, is an exercise in comparing testimony with known truth (gravity) and rejecting it for inconsistency with that known truth.

One great advantage of jurors over judges is their diversity of experiences. We judges tend to be ignorant about much that was testified to in this. case. It would be hard to find a judge who nails his own apartment doors shut, has any personal experience with crack or transvestite prostitutes, or visits strangers by coming up the fire escape and tapping on their window. Judges are drawn from a particularly well behaved group of people of limited experience. Fortunately, jurors are more diverse in their experiences than we are. That these experiences include the practice of medicine, as well as the practice of the varied types of conduct of the witnesses in this case, is all the more helpful. Ideally, at least someone on a jury of twelve will be able to contribute to the rest of the jury some useful understanding about whatever evidence comes up. It is probably impossible for a person who has highly relevant experience to evaluate the credibility of witnesses without that experience bearing on the evaluation. Were we to require the impossible and prohibit jurors from relying on relevant, past personal experience, about all we would accomplish would be to induce jurors to lie about it when questioned afterward, unless we limited jury participation to the most unworldly and ignorant individuals.

That is not to say that all juror experience is proper grist for the deliberative mill. A foreman’s speculation about likely sentencing, particularly where the speculation is likely to be prejudicial to the defendant, is error even where there is not some specific, tangible extrinsic evidence introduced into deliberations. First, the introduction of extrinsic evidence involving sentencing into jury deliberations is error. Second, the simple fact that a juror statement is based upon past personal experience does not immunize it from Sixth Amendment inquiry.

We share the Silva and Bayramoglu courts’ concerns regarding speculation about sentencing by jurors, because such speculation may distort their evaluation of the evidence regarding guilt. However, such speculation was also the subject of the routine admonition by the judge in the instructions, “do not discuss or consider the subject of penalty or punishment. That subject must not in any way affect your verdict.” Having been so admonished, the other jurors were well armed to disregard the remark, and to remind the foreman that she should not decide the case based on what she thought would happen after sentencing. We ordinarily assume that the jurors follow their instructions. The remark is much like the remarks, or, at the least, unexpressed assumptions, that jurors routinely make about punishment in criminal cases and insurance in civil cases. That is why the admonition is generally given.

Grotemeyer argues that the state courts unreasonably applied Supreme Court precedent in denying his request for an evidentiary hearing (Grotemeyer did not request an evidentiary hearing in the district court ). The precedent Grotem-eyer offers in support of his claim, Rem mer v. United States, does not require an evidentiary hearing. As Grotemeyer states in his brief: “The Supreme Court has made it clear that where ... jurors discussed potentially prejudicial extrajudicial information, a hearing ... is required.” Because no impermissible extrinsic evidence was discussed, the state court did not act improperly by denying the motion for a new trial without holding an evidentiary hearing.

Grotemeyer also argues that he should have received a state-court eviden-tiary hearing on his ineffective-assistance-of-counsel claim. He alleges that he was deprived of effective assistance because his lawyer did not interview the music-hater before trial and failed to learn of the things the witness later said in his affidavit. Assuming without deciding that his lawyer should have interviewed the witness before trial in order to meet the Strickland standard, there was no prejudice. Even had the music-hater been permitted to testify as to the inconsistency between the victim’s demeanor and that of rape victims generally (he did not testify to any experience with rape victims generally that would give him foundation for this opinion), and of her invitation to smoke some sort of drug and drink wine with her, it is hard to see how it could make any difference. The victim’s frenzied box-piling against her apartment door and her physical injuries corroborated her account that Grotemeyer was an uninvited intruder and aggressor. The mental condition obvious from Grotemeyer’s door-nailing and brain damage from his car accident, and the unlikelihood of Grotemeyer’s claim that he was peacefully masturbating in his own apartment when the victim walked in on him, that she induced him to come to her apartment, and that she induced him (despite his own lack of enthusiasm) to inflict on her the torn clothes, cuts and bruises, and rectal penetration she suffered, were not in any way diminished by the music-hater’s affidavit. The statements in the affidavit that the victim was a liar, which he inferred from her continuing to play classical music on her piano despite her supposed agreement not to do so except during restricted times, would more likely persuade the jury that the music-hater had an unusually strong dislike for music than that the victim was a liar.

Conclusion

Varied juror experience is a virtue that assists juries in ascertaining the truth. The California Court of Appeal decision was not contrary to or an unreasonable application of clearly established federal law as determined by the Supreme Court. The district court properly denied the petition for a writ of habeas corpus.

AFFIRMED.

. In re Malone, 12 Cal.4th 935 , 50 Cal.Rptr.2d 281 , 911 P.2d 468, 486 (1996). . People v. Hosler, 16 Cal.4th 561 , 66 Cal.Rptr.2d 454 , 941 P.2d 87, 99 (1997). . In re Carpenter, 9 Cal.4th 634 , 38 Cal.Rptr.2d 665 , 889 P.2d 985, 995-98 (1995). . Irvin v. Dowd, 366 U.S. 717, 722 , 81 S.Ct. 1639 , 6 L.Ed.2d 751 (1961). . Pennsylvania v. Ritchie, 480 U.S. 39, 51 , 107 S.Ct. 989 , 94 L.Ed.2d 40 (1987) (“The Confrontation Clause provides two types of protections for a criminal defendant: the right physically to face those who testify against him, and the right to conduct cross-examination.”) . Turner v. Louisiana, 379 U.S. 466 , 85 S.Ct. 546 , 13 L.Ed.2d 424 (1965). . United States v. Navarro-Garcia 926 F.2d 818, 821-22 (9th Cir. 1991) (noting instances in which "a juror’s personal experiences may constitute extrinsic evidence”); Bayramoglu v. Estelle, 806 F.2d 880, 887 (9th Cir. 1986) ("Jurors have a duty to consider only the evidence which is presented to them in open court.”). . Turner, 379 U.S. at 472-73 , 85 S.Ct. 546 (quoting Irvin, 366 U.S. at 722 , 81 S.Ct. 1639 ). . See Bayramoglu, 806 F.2d at 887-89 (9th Cir. 1986) (analyzing juror misconduct separately from juror bias). . Compare Delaware v. Van Arsdall, 475 U.S. 673, 684 , 106 S.Ct. 1431 , 89 L.Ed.2d 674 (1986) (holding that Confrontation Clause violations are subject to harmless-error analysis), with Dyer v. Calderon, 151 F.3d 970 , 973 & n. 2 (9th Cir. 1998) (en banc) ("The presence of a biased juror cannot be harmless; the error requires a new trial without a showing of actual prejudice.”). . See Koerner v. Grigas, 328 F.3d 1039, 1052 (9th Cir.2003). . 28 U.S.C. § 2254 (d)(1). The AEDPA ground of "unreasonable determination of the facts in light of the evidence presented” is not raised in this appeal. . Parker v. Gladden, 385 U.S. 363 , 87 S.Ct. 468 , 17 L.Ed.2d 420 (1966). . Turner, 379 U.S. at 472-73 , 85 S.Ct. 546 . . Navarro-Garcia, 926 F.2d at 820 . . Bayramoglu, 806 F.2d at 882 . . 1A Kevin F. O'Malley, Jay E. Grenig & William C. Lee, Federal Jury Practice and Instructions § 12.03 (5th ed.2000) (emphasis added). . Navarro-Garcia, 926 F.2d at 821 . . Id. (quoting Kessler, "The Social Psychology of Jury Deliberations,” in The Jury System in America 69, 83 (Rita J. Simon ed., 1975)). . , 9 Wigmore on Evidence § 2570 (Chad-bourn rev. 1981). . Sea Hawk Seafoods, Inc. v. Alyeska Pipeline Serv. Co., 206 F.3d 900 , 912-13 (9th Cir. 2000). . Bayramoglu, 806 F.2d at 887-88 (unless properly mitigated, discussion of possible sentence is impermissible extrinsic evidence); Silva v. Woodford, 279 F.3d 825, 834 (9th Cir.2002) (juror discussion of the possibility of parole for the defendant introduces impermissible extrinsic evidence and raises a risk of constitutional defect serious enough to warrant issuance of a "certificate of appealability”). . Mach v. Stewart, 137 F.3d 630 (9th Cir. 1997); Mancuso v. Olivarez, 292 F.3d 939, 951 (9th Cir.2002). . See Lawson v. Borg, 60 F.3d 608, 611 (9th Cir. 1995) (stating that an evidentiary hearing before the federal district court is appropriate if a habeas petitioner did not receive a full and fair hearing in state court). . Remmer v. United States, 347 U.S. 227, 228, 230 , 74 S.Ct. 450 , 98 L.Ed. 654 (1954) (vacating and remanding for a hearing a case in which the jury foreman had allegedly been offered a bribe, the FBI investigated, and the judge and prosecution discussed the FBI’s report without informing defense counsel, who "first learned of the matter by reading of it in the newspapers after the verdict”). . Strickland v. Washington, 466 U.S. 668, 690, 694 , 104 S.Ct. 2052 , 80 L.Ed.2d 674 (1984). . 28 U.S.C. § 2254 (d)(1).