Discussion:
Q1: 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.
(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.
Q2: 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.
Q3: 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?
Table: Number of boys in family of eight children
Number of boys per Empirical Empirical Relative
Family of young Frequency Frequency
Children (number of families) of families
0 215 0.040
I 1. 415 0.0277
2 5, 331 00993
3 10.649 0.1984
4 11.959 02787
5 11.929 02222
6 6.678 0.1244
7 2.092 0.0190
8 342 0.0064
Total 53.680 10000