Question

Independent random samples, each containing 50 observations, were selected from two populations. The samples from populations 1 and 2 produced 31 and 25 successes, respectively. Test H0:(p1−p2)=0 against Ha:(p1−p2)≠0. Use α=0.05.

(a) The test statistic is

(b) The P-value is

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 = 31 / 50 = 0.62

₂ = x₂ / n₂ = 25 / 50 = 0.5

= (x₁ + x₂) / (n₁ + n₂) = (31 + 25) / (50 + 50) = 0.56

1 - = 0.44

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

Z = (0.62 - 0.5) / 0.56 * 0.44 * (1 / 50 + 1 / 50)

Z = 1.209

Test statistic = 1.21

P(z > 1.21) = 0.1131

P-value = 2 * 0.1131 = 0.2262