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 1 error is chosen to be zero. Without performing 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 1% significance level, can you conclude that the current mean annual salary of professors at this university is more than $55,648?