Problem:

A company has administrated a brief test to all 10,000 personel. The mean score for all is 50 with a standard deviation of 10 a researcher wishes to invetigate the theory that supervisors score higher on test than managers. to test this theory he selected a random sample of 400 first line supervisors and finds thge mean score to be 52.

Required:

Question 1) Test the hypothesis that supervisors score higher than managers use a Z critical of 2 standard scores to test this hypothesis ( alpha=.0228)

1) state hypothesis

2) choose test statistic

3)identify critical score

4) identified computed score

5) decision rule

Question 2) suppose that the actual mean score for all supervisors is 52 what is the probability that the decision rule will lead to a correct decision, what is the power of the test?

Solve the problem and show all work.