Sparr Investments, Inc., specializes in tax-deferred investment opportunities for its clients. Recently Sparr offered a payroll deduction investment program for the employees of a particular company. Sparr estimates that the employees are currently averaging $100 or less per month in tax-deferred investments. A sample of 40 employees will be used to test Sparr's hypothesis about the current level of investment activity among the population of employees. Assume the employee monthly tax-deferred investment amounts have a standard deviation of $75 and that a .05 level of significance will be used in the hypothesis test.
a. What is the Type II error in this situation?
b. What is the probability of the Type II error if the actual mean employee monthly investment is $120?
c. What is the probability of the Type II error if the actual mean employee monthly investment is $130?
d. Assume a sample size of 80 employees is used and repeat parts (b) and (c).