a sociologist is dealing with a certain population with an unknown mean number of years of education and standards diviation of 2.25. he is testing the hypothesis that the population mean is 13.5 years, so she surveyed a sample of 100 residents. He decides to reject the null hypothesis when the mean is greater than or equal to 14 years.

a. what is the probability that sociologist commits a type I error?

b. if the sociologist is not aware that that population means is 14.5 years, what is his probability of committing type II error?

c. determine the power of the test?​