Question

In a survey of 350 childless married couples who were asked if they plan to have children in the next 55 years, 18% of the men and 10% of the women responded "Yes". Based on this survey, can it be concluded that there is a difference in the proportion of men ( p1) and women ( p2 ) responding "Yes"? Use a significance level of α=0.05 for the test.

Step 1 of 5: State the null and alternative hypotheses for the test.

Step 2 of 5: Compute the weighted estimate of p, p‾p‾. Round your answer to three decimal places.

Step 3 of 5: Compute the value of the test statistic. Round your answer to two decimal places.

Step 4 of 5: Find the P-value for the hypothesis test. Round your answer to four decimal places.

Step 5 of 5: Make the decision to reject or fail to reject the null hypothesis.

Answer 1

The statistical software output for this problem is:

From above output:

Step - 1: Hypotheses:

H₀ : p₁ - p₂ = 0
H₁ : p₁ - p₂ ≠ 0

Step - 2: p = (63 + 35)/(350 + 350) = 0.140

Step - 3: Test statistic = 3.05

Step - 4: p - Value = 0.0023

Step - 5: Reject Null Hypothesis