# Bio statistics: Chi-square & Exact two-sided P-value

6.23 Fisher [1958] presented data of Geissler [1889] on the number of male births in German families with eight offspring. One model that might be considered for these data is the binomial distribution. This problem requires a goodness-of-fit test.

(a) Estimate Π, the probability that a birth is male. This is done by using the estimate p = (total number of male births)/(total number of births). The data are given in Table 3.10.

Table is given in the attachment.

(b) Using the p of part (a), find the binomial probabilities for number of boys = 0, 1, 2, 3, 4, 5, 6, 7 and 8. Estimate the expected number of observations in each cell if the binomial distribution is correct.

6.4 Ounsted [1953] presents data about cases with convulsive disorders. Among the cases there were 82 females and 118 males. At the 5% significance level, test the hypothesis that a case is equally likely to be of either gender. The siblings of the cases were 121 females and 156 males. Test at the 10% significance level the hypothesis that the siblings represent 53% or more male births.

6.2 In a dietary study, 14 of 20 subjects lost weight. If weight is assumed to fluctuate by chance, with probability ½ of losing weight, what is the exact two-sided p-value for testing the null hypothesis Π = 1/2?

See Attachment 3.10 attached.

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#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis and exact two-sided p-value. Formula for the calculation and Interpretations of the results are also included.