The speed of cars (mph or miles/hour) on CA-60 freeway follows a normal distribution. A highway safety researcher believes that cars on CA-60 travel at an average speed of 70 mph. From a sample of 11 vehicles driving on the highway, he finds the sample average speed to be 74.5 mph with a sample standard deviation of 9 mph.
a. Use a t-test to verify his belief
b. Suppose that the population standard deviation is known to be 15. Use a suitable test at 5% level of significance to verify the hypothesis mentioned in part (a). Explain.