Sparr Investments, Inc. specializes in investment opportunities for its tax-deferred clients. You just offered an investment program with payroll deduction for employees of a certain company. Sparr estimates that right now employees have $ 100 or less per month in tax-deferred investments. To test Sparr's hypothesis about investments among the employee population, a sample of 40 employees is taken. Assume that the monthly amounts invested by employees in tax-deferred investments have a standard deviation of $ 75 and that 0.05 will be used as the significance level in this hypothesis test. Required:
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).