6.23 Fisher  presented data of Geissler  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  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.
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.