Question

A two-sample z-test for two population proportions is to be performed using the P-value approach. The null hypothesis is  and the alternative is . Use the given sample data to find the P-value for the hypothesis test. Give an interpretation of the p-value.

A poll reported that 30% of 60 Canadians between the ages of 25 and 29 had started saving money for retirement. Of the 40 Canadians surveyed between the ages of 21 and 24, 25% had started saving for retirement.

A: P-value = 0.5824; There is about a 58.24% chance that the two proportions are equal.

B: P-value = 0.1812; If there is no difference in the proportions, there is about a 18.12% chance of seeing the observed difference or larger by natural sampling variation.

C: P-value = 0.2912; There is about a 24.96% chance that the two proportions are equal.

D: P-value = 0.2912; If there is no difference in the proportions, there is about a 24.96% chance of seeing the exact observed difference by natural sampling variation.

E: P-value = 0.5824; If there is no difference in the proportions, there is about a 58.24% chance of seeing the observed difference or larger by natural sampling variation.

Answer 1

The statistical software output for this problem is :

P-value = 2 * P(z > 0.55) = 0.5824

E: P-value = 0.5824; If there is no difference in the proportions, there is about a 58.24% chance of seeing the observed difference or larger by natural sampling variation.