Question

I want to conduct the following test at the α=0.01 level of significance by determining the null and alternative hypotheses, the test statistic, and the p-value. These samples were obtained independently using simple random sampling. Test whether p1≠p2. Sample data are: x1=28, n1=255, x2=38, and n2=301

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 = 28 / 255 = 0.1098

₂ = x₂ / n₂ = 38 / 301 = 0.1262

= (x₁ + x₂) / (n₁ + n₂) = (28 + 38) / (301 + 255) = 0.1187

1 - = 0.8813

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

Z = (0.1098 - 0.1262) / 0.1187 * 0.8813 (1 / 255 + 1 / 301)

Z = -0.597

Test statistic = -0.597

P(z < -0.597) = 0.2753

P-value = 2 * 0.2753 = 0.5506