This is an appeal from a judgment of the circuit court for Walworth county, Circuit Judge John R. Race, declaring W.T.D. to be the father of A.M.C., a minor.1 The court of appeals certified the appeal pursuant to sec. 808.05 (2) and sec. (Rule) 809.61, Stats., 1985-86.
The court of appeals certified the following question: "Did the trial court err in relying upon the results of an HLA test, in the absence of independent evidence, to determine that the mother and the alleged father had intercourse during the conceptive period.?”2
*624We disagree with the court of appeals that the case presents this question. The circuit court did not rely on the results of the HLA test to determine whether the mother and putative father had intercourse during the conceptive period.
Rather, this case presents two issues. The first issue is whether the circuit court’s determination of paternity should be reversed because the circuit court misinterpreted a statistical probability that an expert witness derived from the HLA data and then relied on this erroneous interpretation of the statistic to decide the issue of paternity.
The expert testified that the odds against the mother choosing two males simultaneously from the population at large who, according to the HLA tests, could be the father of the child were 1 in 580,000. The circuit court mistakenly interpreted this testimony to mean that the odds against the mother choosing one male biologically able to be the father of the child were 1 in 580,000. The circuit court then relied on this mistaken interpretation of the expert’s one in a half-million calculation to find that W.T.D. lied when he denied having had intercourse with the mother during the conceptive period.
We conclude that the circuit court erroneously interpreted the statistical testimony of the expert witness and that the circuit court afforded this erroneous interpretation substantial weight. Because the circuit court’s reliance on this erroneous interpre*625tation permeates the circuit court’s determination of paternity, we reverse the judgment and remand the case to the circuit court.3
The second issue is whether the fact-finder, be it circuit judge or jury, can decide, as this circuit court did, that the date of sexual intercourse between the mother and putative father is a date other than one claimed by either of the parties. W.T.D. argues that the circuit court’s finding that conception occurred on a date other than the one the mother asserted cannot be sustained by this court because the finding is contrary to the great weight and clear preponderance of the evidence or, stated another way, clearly erroneous. State ex rel. Skowronski v. Mjelde, 112 Wis. 2d 110, 114, 332 N.W.2d 289 (Ct. App. 1983), citing State ex rel. Isham v. Mullally, 15 Wis. 2d 249, 255, 112 N.W.2d 701 (1961); sec. 805.17(2), Stats. 1985-86.4
We conclude that the circuit court could believe the mother’s claim that she had intercourse with the defendant and could reasonably infer that the mother was mistaken about the date and that intercourse occurred at another time. Because the circuit court *626did not make these inferences and instead based its findings on its erroneous interpretation of the statistical evidence, we reverse the judgment.
hH
The following facts were elicited at trial.
The mother testified that she had intercourse only once with W.R.D. from January through April 1985 and that was on March 9,1985. She testified she was certain of the date of intercourse because she signified the act with a "W” on her calendar. She also testified that from January 1985 through April 1985 she did not have intercourse with anyone other than W.T.D.
W.T.D. testified that he did not have sexual intercourse with the mother from January through April 1985.5
The mother gave birth on October 27, 1985, to a child weighing 3 pounds, 9 ounces. Because the child’s birth weight was less than 5 pounds, 8 ounces,6 the *627state attempted to prove the conceptive period through the testimony of doctors. A specialist in obstetrics and gynecology, Dr. Wetzler, testified that the baby’s gestational age was between 31 and 33 weeks and that in his opinion to a reasonable degree of medical certainty the baby was conceived between March 10 and March 24. He testified that the mother had been in his office for a pregnancy test on March 28, 1985, and that she had tested negative. The manufacturer guarantees that the pregnancy test is 100 percent accurate if the woman is at least ten days pregnant. According to the test results and the manufacturer’s guaranty, the child was conceived after March 18.
On cross-examination and examination by the court, however, Dr. Wetzler testified that the pregnancy test made it very unlikely that the child was conceived before March 18,1985, and that it would be extremely rare for a sperm to survive from March 9 to March 18 in the woman’s body; 7- to 10-day survival rates are rare. On redirect and over strong objection, the doctor testified that it was possible the child was conceived on March 9, 1985.
Dr. Schneider, who assumed medical responsibility for the child hours after birth, testified that, according to the "obstetrical wheel,” a child conceived on March 9 and born on October 27 and would have a gestational age of 35-% weeks. He testified further that in his medical judgment, this child’s gestational age could not have been 35 weeks at birth. Initially he assessed the child’s gestational age to be 30 to 32 weeks. His final estimate of the child’s gestational age appears to be 31 to 32 weeks. Finally he explained that a gestational age of 34 weeks at birth places the child’s date of conception on March 17-18 and that a *62832-week gestational age at birth places conception on March 31.
The "one in a half million” statistical evidence in question on appeal was presented by Dr. Barwick, a human geneticist and the state’s expert witness on HLA testing.7 We summarize his testimony to demonstrate how he used the statistic.
Dr. Barwick explained that the paternity index in this case is 764 to 1. This index, he said, means that out of every 765 males chosen from the population at random, odds are that one of them would be genetically capable of fathering the child in question. Dr. Barwick further explained that if 1,530 males were selected at random, chances are that two of them would be genetically capable of fathering the child.
Dr. Barwick further testified that the chances of a woman choosing two males on the first try who would be able to contribute the necessary genetic characteristics to produce the child are over 580,000 to 1. He did not explain how he reached this figure. Apparently this figure is generated as follows: Because 1 in 765 men chosen at random could be the father, the chances of simultaneously selecting two men at random who could be the father would be 1 in 765 and 1 in 765 or 1 in 7652, which is approximately 1 in 580,000.
The circuit court used this "1 in 580,000” statistic to decide whether W.T.D. had intercourse with the mother during the conceptive period (as calculated by the doctors) and whether he was the father of the child.
*629In summing up the evidence at the close of trial, the circuit court found that a 3-pound, 9-ounce baby was born out of wedlock on October 27,1985; that the child was conceived on approximately March 31,1985; and that W.T.D. and the mother had intercourse on or about that date. The circuit court stated that it disbelieved the mother’s testimony about the date of intercourse being March 9, 1985, and it disbelieved W.T.D.’s denial of sexual intercourse with the mother from January through April 1985, concluding that "the odds were simply not there.” The circuit court found that "the possibility or odds that [the mother] could pick a man other than the biological father and come up with the putative father is about one chance in a half-million.” Later, the circuit court stated that it disbelieved W.T.D.’s testimony "because there’s only one chance in 580,000 that he could be chosen at random to be the father.”
II.
The court of appeals described the issue as whether the circuit court erred in relying on the results of the HLA test. As we stated previously, the appeal does not present this issue. The circuit court did not rely directly on the results of the test. Rather it relied exclusively on a statistic that it mistakenly derived from the testimony.
The circuit court interpreted the expert as saying that the odds that the mother in this case could correctly select at random a man who could be the biological father are about one chance in a half-million. This interpretation is inconsistent with the expert’s testimony. The expert testified that the odds of choosing a man at random with the genetic make*630up to produce the child in question are 765 to 1, not 580,000 to 1.
The expert testified that the odds against randomly choosing two males who could potentially be the father are astronomical. The statistic emphasizes the unlikelihood that a woman could choose two putative fathers simultaneously and on the first try. The statistic cannot be used to conclude, as the circuit court did, that the mother had only one chance in a half-million of choosing at random a man who biologically could be the father. The astronomical odds against the mother simultaneously and on the first try selecting two putative males from the population at random is not probative on the issue of whether W.T.D. is the father.
The circuit court relied solely on the 1 out of 580,000 statistic to decide the credibility of the mother and W.T.D. and to determine paternity. We conclude that the circuit court’s error in relying on this statistical evidence permeates the circuit court’s finding of paternity and affects the defendant’s substantial right to have the issues of paternity proven by a clear and satisfactory preponderance of the evidence. Secs. 767.47 (8), 805.18 (2), Stats. 1985-86; State v. Schumacher, 144 Wis. 2d 388, 424 N.W.2d 672 (1988). We therefore reverse the judgment and remand the cause to the circuit court for proceedings consistent with this opinion.
HH HH HH
A second issue in this case is whether the fact-finder, be it judge or jury, can decide that the date of sexual intercourse between the mother and putative *631father was a date other than the one asserted by either of the parties.
The elements of a prima facie case in a paternity action are proof of the birth out-of-wedlock, the date of birth, weight at birth, the conceptive period, an accusation that the defendant had sexual relations with the complainant during the conceptive period, and the complainant’s denial that she had sexual relations with another man during the conceptive period. The testimony of the complaining witness that she had intercourse with the defendant and with no one else during the conceptive period is sufficient to sustain the verdict that the defendant is the father if the fact-finder believes the testimony. State ex rel. Skowronski v. Mjelde, 112 Wis. 2d 110, 115-116, 332 N.W.2d 289 (Ct. App. 1983).
In this case the circuit court found that conception occurred on March 31, even though the mother testified that intercourse occurred on March 9, 1985. W.T.D. denied any intercourse from January through April 1985 and argues that the circuit court’s finding that conception occurred on March 31 is based on conjecture and speculation. W.T.D. relies on Menn v. State, 132 Wis. 61, 112 N.W. 38 (1907), in which the supreme court reversed the verdict of paternity.
In Menu the mother testified that on Sunday, October 16, 1904, "most positively” — and at no other time — did she and the defendant have intercourse. She offered evidence showing the impossibility of intercourse on any other Sunday evening within the period of possible conception. At the close of trial, the judge instructed the jury that if it did not find that sexual intercourse had taken place on October 16, 1904, the defendant is entitled to acquittal unless it *632found from the evidence that the defendant did have sexual intercourse with the complainant at some other time and place within the gestation period. Menu, 132 Wis. at 63. There was no evidence of intercourse at any other time and the trial court so viewed the evidence. The trial court further instructed the jury that "the date of the act of sexual intercourse between the complaining witness and the defendant is an important fact in this action, and there is no evidence that it occurred at any time except on the 16th of October, 1904 .... The jury must decide this case upon the evidence given in court, and have no right to guess or speculate as to what the facts might be outside the evidence.” Menn, 132 Wis. at 63.
The supreme court reversed the judgment. First the court noted that the instructions given to the jury were "hopelessly inconsistent. The jury were told at first that they could not guess or conjecture, and later that they need not acquit if they did guess or conjecture” about the date of intercourse. Menn, 132 Wis. at 63-64. The court concluded that it was "prejudicial error to instruct the jury directly or by implication that it could cast loose from the evidence and guess or conjecture that some event occurred as to which evidence is entirely wanting.” Menn, 132 Wis. at 64. The supreme court reasoned that because both the complainant and the defendant denied intercourse occurred on any other date and because the complainant failed to testify that she did not have sexual intercourse with any other male during the conceptive period, there was no credible evidence to establish intercourse on a date other than the date claimed by the complainant. If the jury did not accept that date, then the complainant did not establish that the defendant was the father.
*633The supreme court recognized in Menu that the complainant need not always establish the exact time or exact circumstances of the act of intercourse; a verdict might be sustained merely upon the fact of pregnancy and testimony that the accused and no one else had intercourse with the complainant. This court said, however, that these facts were lacking in the Menn case, 132 Wis. at 64-65.
The state argues that it must prove not the exact date of sexual intercourse but that intercourse occurred during the conceptive period and that the infant was the result of that act. The state asserts that the fact-finder may find that the mother is mistaken about the exact date of intercourse and conclude that intercourse occurred on a different date. The state relies on Stresney v. State ex rel. Bean, 186 Wis. 214, 202 N.W. 334 (1925), and State ex rel. Dewey v. Kibble, 186 Wis. 210, 202 N.W. 333 (1925).
In both Stresney and Dewey, the mother testified that intercourse occurred on a particular date and denied having intercourse with another male during the conceptive period; the defendant in each case denied having sexual intercourse with the mother on the date or dates in question and presented testimony challenging the mother’s assertions. In each case the trial court approved a jury instruction to the effect that the complainant need not prove the exact date of intercourse as long as the complainant proves that the act of intercourse actually occurred and resulted in the birth of the child. Dewey, 186 Wis. at 211; Stresney, 186 Wis. at 216.
In Dewey, the mother testified that she had intercourse with the defendant on April 2, 1922. The defendant presented alibi evidence. The trial court instructed the jury that the state need not prove the *634exact date of intercourse; intercourse must be shown to have occurred on such a date as would satisfy the jury that the infant was the result. Dewey, 186 Wis. at 211. After the jury found that the defendant was the father, the trial court, relying on Menn, ordered a new trial on the ground that the instruction might have erroneously conveyed the impression that the jury might disbelieve the mother as to the only date she testified intercourse occurred and might conclude that intercourse occurred on some other occasion. On appeal this court upheld the jury verdict, concluding that the jury, having weighed all the evidence, could conclude that the complainant may have been mistaken about the exact date of intercourse, but not about the act of intercourse. Dewey, 186 Wis. at 212.
In Stresney, the mother testified that sexual intercourse between herself and the defendant occurred on March 20 and March 21. She said she remembered these dates because a couple of weeks after intercourse occurred she left her job at a bakery where she had met the defendant. The bakery’s records revealed that the mother began work on May 18 and left on July 31. The defendant argued that her testimony that intercourse occurred on March 20-21 was not to be believed and there was no competent, credible evidence upon which to conclude that he was the father. Stresney, 186 Wis. at 215. The trial court instructed the jury that although the mother may be mistaken about the exact daté of intercourse, the jury could find the defendant to be the father if it was satisfied that sexual intercourse actually took place and resulted in the birth of the child. The jury found the defendant to be the father. On appeal, this court affirmed the verdict, reasoning that the jury may have questioned the correctness of the bakery’s records or *635given them full credence and concluded that the mother was mistaken about the dates of her employment, but not about the time and place of intercourse. 186 Wis. at 216.
The Dewey and Stresney courts distinguished the Menu case. The Dewey court noted, without elaboration, that the Menu decision was decided prior to the enactment of the harmless error statute, now sec. 805.18 (2), Stats. 1985-86. Dewey, supra 186 Wis. at 211.
The Stresney court stated that the instruction in Menn permitted the jury to bring in a verdict which was based on an act for which there was no testimony, while the instruction in Stresney permitted the jury to convict if it found the acts to which the mother had testified had taken place although the mother was mistaken about the exact date. The Stresney court concluded:
"In [the Menn case] there was no other act of intercourse testified to but the one of October 16, 1904, and yet the court told the jury they could convict upon an act not testified to at all. Of course that was prejudicial error. In the case at bar the court simply told the jury that though the complaining witness might have been mistaken as to the exact date of intercourse, nevertheless if they found that the acts which she testified to actually took place and resulted in the birth of the child they could convict though there might be doubt as to their exact date. Such is the law, and such an instruction is radically different from one saying you may convict upon acts not testified to at all, as was the one given in the Menn case.” Stresney, at 216-17.
*636Thus, Stresney and Dewey, which distinguish Menu, stand for the proposition that if the fact-finder believes the act of intercourse to which the mother testified actually took place, the fact-finder might disbelieve the witness about the date of intercourse and determine that intercourse took place at another date.
These cases are consistent with the general rules applicable to fact-finding. We have often said that the fact-finder might believe parts of a witness’s testimony and disbelieve other parts and that the credibility of a witness is peculiarly a matter for the trier of fact. Brown v. Wisconsin Natural Gas Co., 59 Wis. 2d 334, 342, 208 N.W.2d 769 (1972). We have further stated that the fact-finder may draw reasonable inferences from credible evidence, and the reviewing court must accept those inferences unless they are against the great weight and clear preponderance of the evidence. Cogswell v. Robertshaw Controls Co., 87 Wis. 2d 243, 249-50, 274 N.W.2d 647 (1979). An inference is reasonable if it can fairly be drawn from the facts in evidence. While an inference cannot be based on speculation or conjecture, the fact-finder might find any fact which it believes might rightfully and reasonably be inferred from the evidence of the case; the inferences should be logical and natural results drawn from the evidence by proper deduction.
According to the record, conception could have occurred as early as March 9, but the negative results of the pregnancy test given on March 28 make it unlikely that the child was conceived prior to March 18. Witnesses estimated the child’s gestational age at birth to be approximately 31 to 32 weeks which places conception on or about March 31.
*637The fact-finder in this case could have reasonably concluded that the conceptive period was between March 9 and March 31 and more probably between March 18 and March 31. There was evidence from which the circuit court could reasonably infer that intercourse occurred on or about March 31, which was within the conceptive period. The mother testified that intercourse occurred on March 9 and that she was certain of this date because she denoted the act with a "W” on her calendar. The mother also testified that she did not have intercourse with another man during the conceptive period. According to the record, W.T.D. and the mother admitted they had sexual intercourse prior to January 1, 1985. The mother testified she and W.T.D. had sexual intercourse once after March 31, 1985. The trier of fact could reasonably have found that the mother was mistaken or lied about the exact date of intercourse and could have inferred from the testimony that the mother and W.T.D. had sexual intercourse in March, sometime after March 9, which resulted in the birth of the child.
The circuit court did not make these inferences. Instead, the circuit court based its findings of paternity on its erroneous interpretation of the statistical evidence. For the reasons we set forth previously, we reverse the judgment and remand the case to the circuit court for further proceedings consistent with this opinion.
By the Court. — The judgment of the circuit court is reversed and the cause remanded.
On November 6,1985, the State of Wisconsin filed a petition on behalf of the mother alleging that W.T.D. is the father of A.M.C., a child born out of wedlock. The family court commissioner ordered blood tests consisting of tests of red blood cells, serum proteins and HLA (human leucocyte antigens) tissue types (T16) for the mother, child and W.T.D. pursuant to sec. 767.48 (1), Stats. 1985-86. See State ex rel. v. Slocum, 109 Wis. 2d 397, 326 N.W.2d 397 (Ct. App. 1982).
W.T.D. waived his right to a jury trial, and the case was tried before the circuit court.
The state introduced into evidence a report from the Roche Biomedical Laboratories of the red cell antigens and leucocyte antigens (HLA) of the mother, the child and W.T.D., the putative father. The report stated the combined paternity index as 764 to 1 and the probability of paternity as 99.86%. The report concluded that W.T.D. "cannot be excluded as the biological father of the *624child ... since they share common genetic markers.” On the basis of the HLA system, along with ABO, Rh, MNSs, Kell, and Duffy, the report states that the probability of paternity is 99.38%, as compared to an untested man of the North American Caucasian population. The HLA test is set forth in sec. 767.48 (1), Stats. 1985-86.
" No judgment shall be reversed or set aside or new trial granted in any action or proceeding on the ground of ... the improper admission of evidence ..., unless in the opinion of the court to which the application is made, after an examination of the entire action or proceeding, it shall appear that the error complained of has affected substantial rights of the party seeking to reverse or set aside the judgment." Sec. 805.18 (2), Stats. 1985-86. See also, State v. Schumacher, 144 Wis. 2d 388, 424 N.W.2d 672 (1988).
Sec. 767.47 (8), Stats. 1985-86, provides that "the party bringing the action for the purpose of determining paternity ... shall have the burden of proving the issues involved by clear and satisfactory preponderance of the evidence.”
W.T.D. attempted to cast doubt on the mother’s credibility by asserting that the mother failed to inform him that he was the father. He also attempted to cast doubt on the statistics derived from the HLA test by showing that he had blood relatives in the geographic area. He testified that his brother frequently visited Lake Geneva and that he had a number of cousins who resided in the Lake Geneva area. W.T.D. never requested any of his male relatives to testify about their sexual relations with the mother or, for that matter, to submit to the blood tests pursuant to secs. 767.48 (1), 767.47 (5), Stats. 1985-86.
If the child weighs five pounds, eight ounces or more at birth, the conceptive period is presumed to be 240 to 300 days before birth unless competent evidence to the contrary is presented. Sec. 891.395, Stats. 1985-86. The presumption has no application in this case when the baby weighs less than five pounds, eight ounces.
Sec. 767.47, Stats. 1985-86, governs evidence relating to paternity and includes medical, scientific, or genetic evidence.