Question

1. In a presidential election, 308 out of 611 voters surveyed said that they voted for the candidate who won. Use a 0.01 significance level to test that among all voters, the percentage who believe they voted for the winning candidate is different from 43%, which is the actual percentage of votes for the winning candidate. What does the result suggest about voter perceptions? Must show all work.

Answer 1

The following information is provided: The sample size is N = 611, the number of favorable cases is X = 308, and the sample proportion is and the significance level is α=0.01

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: p = 0.43

Ha: p ≠​ 0.43

This corresponds to a two-tailed test, for which a z-test for one population proportion needs to be used.

(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 z_c = 2.58

(3) Test Statistics

The z-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that |z| = 3.699 > z_c = 2.58, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0.0002, and since p = 0.0002 < 0.01, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population proportion pp is different than p_0 ​, at the α=0.01 significance level.