According to a Bureau of Labor Statistics release of March 25, 2015, financial analysts earned an average of $110,510 in 2014. Suppose that the 2014 earnings of all financial analysts had a mean of $110,510. A recent sample of 400 financial analysts showed that they earn an average of $114,630 a year. Assume that the standard deviation of the annual earnings of all financial analysts is $30,570.
a. Using the critical-value approach, can you conclude that the current average annual earnings of financial analysts is higher than $110,510? Use α = .01.
b. What is the Type I error in part a? Explain. What is the probability of making this error in part a?
c. Will your conclusion of part a change if the probability of making a Type I error is zero?
d. Calculate the p-value for the test of part a. What is your conclusion if α = .01?