## Power

Hi, I'm having trouble with getting started these two problems and would appreciate any help

In an attempt to reduce the number of person-hours lost as a result of industrial accidents, a large production plant installed new safety equipment. In a test of the effectiveness of the equipment, a random sample of 43 departments was chosen. The number of person-hours lost in the month prior to and the month after the installation of the safety equipment was recorded and the percentage change was calculated. Find the power of the test designed to determine if the the new safety equipment is effective when the mean percent reduction is actually 0.8%. Assume that the population standard deviation is 10% and that alpha is 0.07.

A dean in the business school claims that GMAT scores of applicants to the school's MBA program have increased during the past 5 years. Five years ago, the mean and standard deviation of GMAT scores of MBA applicants were 550 and 55, respectively. 24 applications for this year's program were randomly selected and the GMAT scores recorded. If we assume that the distribution of GMAT scores of this year's applicants is the same as that of 5 years ago, find the probability of erroneously concluding that there is not enough evidence to support the claim when, in fact, the true mean GMAT score is 580. Assume alpha is 0.03.