Exam time The professor of a large math class estimates that at the intended level of difficulty, his undergraduate midterm exams require on average 10 minutes for graduate students in his department to complete. If the average is longer than 10 minutes, then the exam is likely too hard and needs to be revised. As usual, the professor gathers his 20 teaching assistants in a room to have them test out the exam. You can assume the teaching assistants comprise a random selection of all graduate students in the department.

Their completion times had an average of 13 minutes, with a standard deviation of 2 minutes.

a) What are the null and alternative hypotheses you should test?

b) In this context, what would a Type I error be?

c) In this context, what would a Type II error be?

d) Compute a 95% confidence interval for the mean sales per store in a week with the new packaging.

e) Using the confidence interval in (d), what are the conclusions of your hypothesis test? At what significance level?