Hypothesis Test: Difference In Proportions - Stat Trek

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Compute the test statistic. The test method is a two-proportion z-test. Since population proportions are hypothesized to be equal, we use the pooled sample proportion (p) to compute the standard error (SE). When we know the standard error, we compute the z-score test statistic (z) required for a two-proportion z-test.

p = (p1 * n1 + p2 * n2) / (n1 + n2)

p = [(0.38 * 100) + (0.51 * 200)] / (100 + 200)

p = 140/300 = 0.467

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }

SE = sqrt [ 0.467 * 0.533 * ( 1/100 + 1/200 ) ]

SE = sqrt [0.003733] = 0.061

z = (p1 - p2) / SE = (0.38 - 0.51)/0.061 = -2.13

where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.

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