In: Statistics and Probability
Let X equal the number of female children in a three-child family. Among students who were taking statistics, 52 came from families with three children. For these families x = 0, 1, 2, and 3 for 5, 17, 24, and 6 families, respectively.
(a) Conduct a Chi-square goodness-of-fit test to test the null hypothesis that the distribution of X is B(3, 0.5) at 0.05 significance level.
(b) Conduct a Chi-square goodness-of-fit test to test the null hypothesis that the distribution of X is B(3, p) at 0.05 significance level. Estimate p.