The mean score for all professionals taking a certification exam in quality management is 81.2 with a standard deviation of 5.1. A professional society offers review courses in preparation for the exam. The mean score of a random sample of 100 people taking the review courses was 82.4.

A. Find the lower limit of the 95% confidence interval for the mean score to one decimal place.

B. Find the upper limit of the 95% confidence interval for the mean score to one decimal place.

C. Find the z-score (step 4) of the hypothesis test at a 5% level that taking the review course improves (one-sided) the scores on the exam to two decimal places.

D. Find the p-value (step 5) of the one-sided hypothesis test at a 5% level that taking the review course improves (one-sided) the scores on the exam to four decimal places.

E. Should you reject the null at the 5% level (yes or no in lower case)?

F. Find the critical value that you use to calculate the power of the one-sided test at =5% against the alternative mean 82.0 to two decimal places.

G. Calculate the power of the test at =5% against the one sided alternative mean 82.0 to four decimal places.

H. How large of a sample must be taken to get a margin of error of 1.0 with 95% confidence?