Another study from the book A Handbook of Small Data Sets (Hand et al., 1993) describes the family structure in the ­Hutterite Brethren, a religious group that is essentially a closed population with nearly all ­marriages involving members of the group. The researchers were interested in studying the ­offsprings of such families. The following data list the distribution of sons in families with seven children.

a. Test the hypothesis that the number of sons in a family of seven children follows a binomial distribution with π = .5. Use a = .05.
b. Suppose that p is unspecified. Evaluate the general fit of a binomial distribution. Using the p-value from your test statistic, comment on the adequacy of using a binomial model for this situation.
c. Compare your results from parts (a) and (b).

Number of Sons Frequency 06 4 25 2 22 9 1