Question

A researcher finds that of 1000 people who said that they attend a religious service at least once a week, 31 stopped to help a person with car trouble. Of 1200 people interviewed who had not attended a religious service at least once a month, 22 stopped to help a person with car trouble. At the 0.05 significance level, test the claim that the two proportions are equal.

Options are:

a)

P-value: p = 0.0268
Because p < alpha, we reject the null hypothesis. There is sufficient evidence to reject the claim that the proportional are equal

b) P-value: p = 0.0537
Because p > alpha, we fail to reject the null hypothesis. There is not sufficient evidence to reject the claim that the proportional are equal

c)P-value: p = 0.9732
Because p > alpha, we fail to reject the null hypothesis. There is not sufficient evidence to reject the claim that the proportional are equal

Answer 1

Ans ) let us consider null and alternative hypothesis

Ho:p1=p2

Ha:p1 p2

using minitab>stat>basic stat>2 proportion

we have

Test and CI for Two Proportions

Sample X N Sample p
1 31 1000 0.031000
2 22 1200 0.018333

Difference = p (1) - p (2)
Estimate for difference: 0.0126667
95% CI for difference: (-0.000486530, 0.0258199)
Test for difference = 0 (vs ≠ 0): Z = 1.93 P-Value = 0.0537

here option b is true

b) P-value: p = 0.0537
Because p > alpha, we fail to reject the null hypothesis. There is not sufficient evidence to reject the claim that the proportional are equal