Problem 5E

Let X equal the number of female children in a three-child family. We shall use a chi-square goodness-off it statistic to test the null hypothesis that the distribution of X is b(3, 0.5).

(a) Define the test statistic and critical region, using an α = 0.05 significance level.

(b) 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. Calculate the value of the test statistic and state your conclusion, considering how the sample was selected.

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