For testing H 0 : 1 = 2 using independent binomial variates y 1 and

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For testing H0: π1 = π2 using independent binomial variates y1 and y2? with n1 and n2 trials, the score statistic is

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where π̂ = (y1 + y2)/(n1 + n2) is the pooled estimate of π1 = π2 under H0. Show that z2 = X2.

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