1. A random sample of n = 36 cars driving on a residential street had a sample mean of 38 miles /hour, and a standard deviation of 12 miles per hour. (a) Obtain a 95% Confidence Interval for the true population mean speed of all drivers on the street. (b) Test whether the population mean speed is different from the posted speed limit of 35 mph with a confidence level of a = 0.05. Make sure to state the null and alternative hypotheses and show all the steps for the test. (c) Use the 95% Confidence interval to test the hypothesis that the mean speed is different from the posted speed limit of 35