A random sample of 100 people was taken.Eighty-five 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 80%.At the .05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is

A) significantly greater than 80%.
B) not significantly greater than 80%.
C) significantly greater than 85%.
D) not significantly greater than 85%.

To determine if the proportion of the population in favor of Candidate A is significantly more than 80%, we perform a one-tailed hypothesis test:

H0: p ≤ 0.80 (null hypothesis - the proportion is not significantly more than 80%)
H1: p > 0.80 (alternative hypothesis - the proportion is significantly more than 80%)

We use a significance level of 0.05, which means we reject the null hypothesis if the p-value is less than 0.05.

To test this hypothesis, we use a one-sample proportion test. The sample proportion is 0.85, and the sample size is 100.

Using a calculator, we find the p-value to be 0.1736. This means that the probability of obtaining a sample proportion of 0.85 or higher, assuming the null hypothesis is true, is 0.1736.

Since the p-value is not less than 0.05, we fail to reject the null hypothesis. Therefore, we can conclude that the proportion of the population in favor of Candidate A is not significantly greater than 80%. The correct answer is B: not significantly greater than 80%.