Question

7. Sparr Investment, Inc., specializes in tax-deferred investment opportunities for its clients. payroll deduction investment program for the employees of a currently averaging $100 or less Recently Sparr offered particular company. Sparr estimates that the employees 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 0.05 level of significance will be used in the hypothesis test. What is the Type II error in this situation? (3%) b. What is the probability of the Type II error if the actual mean investment is $120? (5%) (Note: without mathematical calculation process, no credit) c. What is the probability of the Type II error if the actual mean employee monthly investment is $130? (5%) (Note: without mathematical calculation process, no d. Assume a sample size of 80 employees is used and repeat parts (b) and (c) to find out the probability of the Type II error. What happens to the probability of making a Type II error when increasing the sample size? Interpret. (7%) (Note: without mathematical calculation process and interpretation, no credit) a are a. employee monthly credit)

Answer 1

Answer a) Турe II eror *Fail to reject a false HO Say Ho when Ha Say mu 100 when in fact mu <= 100 Answer: Concluding that the employees are averaging $100 or less per month in tax-deferred investments (Ho) when in fact they are averaging more than $100 per month in tax-deferred investments (Ha)

b) ) Find the xbar critical value - the value that separates the rejection region from fail to reject region xbar Ho value +z sigma/sqrt(n) xbar 100 1.645* 75 / sqrt(40) xbar 119.507 ii Find the z-score for the xbar critical value using the true value for mu z=(xbar-mu)/(sigma/sqrt(n)) z=(119.507-120)(75/sqrt(40)) z=-04 (ii Find the probability that z< -04 (since we are testing greater than) V beta P(xbar crit 119.507 given mu = 120) beta P(z<-04) beta 4840

c) xbar 1001.645*75/sqrt(40)= 119.507 z (119.507-130) (75/sqrt(40))-88 beta 1894 d) *When mu 120 and n 80 xbar 1001.645* 75/ sqrt(80) 113.794 z (113.794-120)/(75/sqrt(80))=-.74 beta 2296 *When mu 130 and n 80 xbar 1001.645 * 75/ sqrt(80) 113.79 z=(113.794-130)(75/sqrt(80))=-1.93| beta 0268