Question

. The ABC company estimates that its employees are currently averaging $100 or less per month in tax-deferred savings. A sample of 50 employees will be used to test ABC's hypothesis about the current level of savings activity among the population of its employees. Assume that the employee tax-deferred savings amounts have a standard deviation of $80 and that a 5% level of significance will be used for the test. What is the probability of making a Type II error if the "True" monthly savings average $125? What is the probability of making a Type I error?

Answer 1

At alpha = 0.05, the critical value is z_0.95 = 1.645

z_crit = 1.645

or, ( - )/() = 1.645

or, ( - 100)/(80/) = 1.645

or, = 1.645 * 80/ + 100

or, = 118.611

P(Type II error) = P( < 118.611)

                          = P(( - )/() < (118.611 - )/()

                           = P(Z < (118.611 - 125)/(80/))

                            = P(Z < -0.56)

                            = 0.2877

P(Type I error) = 0.05