Use Excel for this problem. Assume the following:

0=0

1=3

=5

a. Demonstrate that if the critical value is held constant, and decrease together as n increases. Use a one-tailed test with a fixed critical value of 1.2. Calculate values for and for n = 1, 2, ..., 100. Plot your results in a graph.

b. Do the same as in part a but use a two-tailed test with fixed critical values of -1.4 and 1.4.

c. Investigate the more usual situation in which is kept constant and the critical value varies with sample size. Keep fixed at 0.05 for this part, and assume a one-tailed hypothesis test with the rejection region in the right tail of the null hypothesis distribution. Determine the critical value for n = 1, 2, ..., 100 when = 0.05. Based on this critical value, determine for each value of n. Plot your results in a graph. How many subjects do you need to achieve 80% power?