An Environmental Protection Agency official asserts that more than 80% of the plants in the northeast region of the United States meet air pollution standards. An antipollution advocate is not convinced by the EPA's claim. She takes a random sample of 64 plants in the northeast region and finds that 56 meet the federal government's pollution standards.
a. Does the sample information support the EPA's claim at the 5% level of significance?
b. For which values of the sample proportion (based on a sample size of 64) would the sample data support the EPA's claim, using a 5% significance level?
c. Would the conclusion found in part a change if the sample proportion remained constant but the sample size increased to 124? Explain why or why not.