Question

I need help to solve this problem: Assume that you plan to use a significance level of alpha=0.05 to test the claim that p 1= 2. Use the given sample sizes and numbers of successes to find the ​p-value for the hypothesis test. n 1=​50, n 2=75 x 1=​20, x 2=15 A. 0.0146 B. 0.0001 C. 0.0032 D. 0.1201

Answer 1

Solution :

Given that,

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ : P₁ = P₂

H_a : P₁    P₂

₁ = x₁ / n₁ = 20 / 50 = 0.4

₂ = x₂ / n₂ = 15 / 75 = 0.2

= (x₁ + x₂) / (n₁ + n₂) = (20 + 15) / (50 + 75) = 0.28

1 - = 0.72

Z = (₁ - ₁) / * (1 - ) (1 / n₁ + 1 / n₂)

Z = (0.4 - 0.2) / 0.28 * 0.72 (1 / 50 + 1 / 75)

Z = 2.44

P(z > 2.44) = 1 - P(z < 2.44) = 0.0073

P-value = 2 * 0.0073 = 0.0146

A)