You are given the following null and alternative hypotheses:

a. If the true population mean is 1.25, determine the value of beta. Assume the population standard deviation is known to be 0.50 and the sample size is 60.
b. Referring to part a, calculate the power of the test.
c. Referring to parts a and b, what could be done to increase power and reduce beta when the true population mean is 1.25? Discuss.
d. Indicate clearly the decision rule that would be used to test the null hypothesis, and determine what decision should be made if the sample mean were 1.23.