Solved: Let p1 denote the proportion of successes in a
Chapter 14, Problem 45E(choose chapter or problem)
Let \(p_1\) denote the proportion of successes in a particular population. The test statistic value in Chapter 8 for testing \(H_0: p_1=p_{10}\) was \(z=\left(\hat{p}_1-p_{10}\right) / \sqrt{p_{10} p_{20} / n}\), where \(p_{20}=1-p_{10}\). Show that for the case k=2, the chi square test statistic value of Section 14.1 satisfies \(\chi^2=z^2\). [ Hint: First show that \(\left(n_1-n p_{10}\right)^2=(n_2-n p_{20})^2\).]
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