Question

In a test for the difference between two proportions, the sample sizes were n₁ = 120 and n₂ = 85, and the numbers of events were x₁ = 55 and x₂ = 45. A test is made of the hypotheses H₀: p₁ = p₂versus H₁: p₁ ≠ p₂.

1. Compute the value of the test statistic.

2. Can you reject H₀ at the α = 0.05 level of significance?

3. Can you reject H₀ at the α = 0.01 level of significance?

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 = 55 / 120 = 0.4583

₂ = x₂ / n₂ = 45 / 85 = 0.5294

= (x₁ + x₂) / (n₁ + n₂) = (55 + 45) / (120 + 85) = 0.4878

1 - = 0.5122

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

Z = (0.4583 - 0.5294) / 0.4878 * 0.5122 (1 / 120 + 1 / 85)

Z = -1.003

Test statistic = -1.003

P(z < -1.003) = 0.1579

P-value = 0.3158

= 0.05

P-value >

Fail to reject the null hypothesis .

= 0.01

P-value >

Fail to reject the null hypothesis .