Exhibit 9-6
A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 75%.
-Refer to Exhibit 9-6. At a .05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is
A)significantly greater than 75%
B)not significantly greater than 75%
C)significantly greater than 80%
D)not significantly greater than 80%

Question

Quizplus · Accepted Answer

We need to conduct a one-sample proportion test. The null hypothesis is that the proportion of the population in favor of Candidate A is equal to 0.75, and the alternative hypothesis is that the proportion is greater than 0.75. Using a z-test with a sample proportion of 0.8, the test statistic is calculated as z = (0.8-0.75)/sqrt(0.75*0.25/100) = 1.33. The critical value for an upper-tailed test at a 0.05 level of significance is 1.645. Since the test statistic is less than the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to conclude that the proportion of the population in favor of Candidate A is significantly greater than 75%.

Exhibit 9-6 a Random Sample of 100 People Was Taken. Eighty of Eighty