The Department of Transportation in Georgia did a study a number of years ago that showed that the proportion of cars that failed to meet the state pollution standard was 0.37. The department would like to be able to say that the cars have improved since then. In a sample of n = 100 cars more recently, the proportion not meeting the standards was 0.28. Are the cars better at meeting the standards than they used to be?
a) Clearly state the null and the alternative hypotheses. Perform the hypothesis test at level ? = 0.01 by computing the test statistic and the p- value.
b) You built your hypothesis testing framework for the proportion 0.37 in (a). Using the same framework, find a proportion value to test for, so that the department is indifferent between rejecting and failing to reject the null hypothesis (i.e., the test statistic is right on the border of the rejection region)?