The Head of Public Safety Notices That the Average Driving

The head of public safety notices that the average driving speed at a particular intersection averages 35 mph with a standard deviation of 7.5 mph.After a school speed limit sign of 20 mph is placed at the intersection,the first 40 cars travel past at an average speed of 32 mph.Using the .01 significance level,was there a significant change in driving speed?
a.Use the five steps of hypothesis testing.
b.Sketch the distributions involved.
c.Advanced topic: Figure the confidence limits for the 99% confidence interval.
d.Explain the logic of what you did to a person who understands hypothesis testing for studies in which the sample consists of a single individual but is unfamiliar with hypothesis testing involving a sample of more than one individual.Be sure your explanation includes a discussion of the distribution of means-what it is,the logic of how it is figured-and its role in the overall hypothesis testing process.Advanced topic: Explain the logic and computation of the confidence intervals.