Question

A two-proportions z-test is to be performed using the  approach. Use the given sample data to find the P-value for the hypothesis test.

x ₁ = 41, n ₁ = 100, x ₂ = 35, n ₂ = 140; H ₀: p ₁ = p ₂, H _a: p ₁ > p ₂ , α = 0.10

		0.4211
		0.0086
		0.0512
		0.0043

Answer 1

Given the hypotheses are:

H₀: p ₁ = p ₂,

H_a: p ₁ > p ₂

Based on the hypothesis it will be right tailed two sample test.

Given details are:

In favour values are:

x ₁ = 41, x ₂ = 35

and the sample sizes are:

n ₁ = 100, , n ₂ = 140

The significance level is α = 0.10

Thus the sample proportions are calculated as:

and the pooled proportion is computed as:

Rejection region:

P-value approach:

Reject the Ho if P-value is less than 0.10.

Test statistic:

P-value:

The P-value is calculated using the excel formula for normal distribution which is =1-NORM.S.DIST(2.627, TRUE), thus the p-value is computed as:

P-value = 0.0043