##### find the P-value for the hypothesis test.

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Assume that you plan to use a significance level of α = 0.05 to test the claim that p1 = p2,  Use the given sample sizes and numbers of successes to find the P-value for the hypothesis test.

n1 = 100    n2 = 100
x1 = 38    x2 = 40
Jul 29th, 2015

Let π be the true population proportion &  p be the sample proportion.

p₁ = 38 / 100 = 0.38
p₂ = 40 / 100 = 0.4

if pc be the pooled proportion.
pc = (38 + 40) / (100 + 100) = 0.39

Ho: π₁ = π₂
Ha: π₁ ≠ π₂

Test statistic:

z = (p₁ - p₂) / √{ [pc(1 - pc)/n₁] + [pc(1 - pc)/n₂] }

= (0.38 - 0.40) / √{ [0.39(1 - 0.39)/100] + [0.39(1 - 0.039)/100] }  = -0.2899

P-value = 2·P(z < -0.2899) = 2·(0.3859) = 0.7718   Answer

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