According to the information obtained from a large university, professors there earned an average annual salary of $55,648 in 1998. A recent random sample of 15 professors from this university showed that they earn an average annual salary of $58,800 with a sample standard deviation of $8300. Assume that the annual salaries of all the professors in this university are normally distributed.
(a) Suppose the probability of making a type I error is chosen to be zero. Without perform- ing all the steps of test of hypothesis, would you accept or reject the null hypothesis that the current mean annual salary of all professors at this university is $55,648?
(b) Using the 1% signi?cance level, can you conclude that the current mean annual salary of professors at this university is more than $55,648?