Verify that the square of the \(Z\) statistic on page 314 equals the \(\chi^{2}\) statistic on page 312 for \(k=2\).

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Statistic for test concerning difference between two proportions X1 X2 n1 - n2 Z = P(1 P(1 - p) + 12 with p= X + X2 = n1+n2 which, for large samples, is a random variable having approximately the standard normal distribution. The test based on this statistic is equivalent to the one based on the x2 statistic on page 312 with k = 2, in the sense that the square of this Z statistic actually equals the x2 statistic (see Exercise 10.38). The critical regions for this alternative test of the null hypothesis p = p2 are like those shown in the table on page 270 with p and p2 substituted for and 2.