A Psychologist has developed a new method designed to help people taking an exam. The method requires the person to come to the office of the Psychologist 5 times over a 5 week period and involves hypnosis and mental exercises. In order to test whether this method is effective the Psychologist carries out the following experiment. He randomly selects 20 subjects and gives them a test. This test is known to have a mean score of 100 when given to the general population. When he gives the test to his subjects after they have gone through his program their scores have a mean of 107.1 with a standard deviation of 12.6

a) Carry out the hypothesis test to see whether or not his method improves the test taking skills by hand (assume that the assumptions are ok, use ?=0.05)

b) Carry out the hypothesis test to see whether or not his method improves the test taking skills using the p-value approach (assume that the assumptions are ok, use ?=0.05)

c) If it were true that using his method the true score goes up to 108, what would be the power of the test?

d) If it were true that using his method the true score goes up to 108, what sample size would be needed to have a power of 95%?

e) Find a 95% confidence interval for the true mean score by hand

f) What sample size would be needed so that the 95% confidence interval for the true mean score has an error of E=2.5?