The average wait time on the phone for taxpayers calling the IRS in 2012 was 1,080 seconds. Suppose (if you can use your imagination) that the IRS made operational changes in an effort to reduce wait times during 2013. To test the effectiveness of these changes, a random sample of 50 phone calls was selected and the wait time of each call was recorded. Assume the standard deviation for the wait time is 250 seconds.

a. Explain in your own words how Type I and Type II errors can occur in this hypothesis test.

b. Using σ = 0.02, calculate the probability of a Type II error occurring if the actual average wait time per call is 1,014 seconds.

c. Using σ = 0.02, calculate the probability of a Type II error occurring if the actual average wait time per call is 960 seconds.

d. Explain the differences in the results you calculated in parts b and c.