A neighborhood has complained that people are speeding through their neighborhood and going on average 45 mph in a 25 mph zone. You think they are exaggerating and so you take a sample of 19 cars driving through the zone and find an average speed of 38 mph with a standard deviation of 17 mph. Test the hypothesis that the average speed in the zone is less than 45 mph at a 95% confidence level.

a) State your hypotheses.

b) Find the critical value for the test statistic.

c) Calculate the test statistic.

d) What is the p-value for your result? Interpret this result in context.

e) Do you reject or fail to reject the null hypothesis? State your answer in context.

f) Calculate a confidence interval for your estimate of the population parameter. Interpret it in context