Question

2 Test the hypothesis that the proportion of men who believe Hillary colluded with the Russians equals the proportion of women who believe Hillary colluded with the Russians.    Use a .01 significance level, a two tail test and the following data:

                                men                        women

students                 110                         100

Hillary colluded    45                           60

Answer 1

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested:

Ho:p1​=p2​

Ha:p1​̸​=p2​

This corresponds to a two-tailed test, for which a z-test for two population proportions needs to be conducted.

(2) Rejection Region: Based on the information provided, the significance level is α=0.01, and the critical value for a two-tailed test is zc​=2.58.

The rejection region for this two-tailed test is R={z:∣z∣>2.58}

(3) Test Statistics

The z-statistic is computed as follows:

(4) Decision about the null hypothesis: Since it is observed that ∣z∣=1.594≤zc​=2.58, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.111, and since p=0.111≥0.01, it is concluded that the null hypothesis is not rejected.

(5) Conclusion: It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion p1​ is different than p2​, at the 0.01 significance level.