During 2012, the average monthly bill for digital cable in the United States was $ 86 according to research firm Centris. Suppose Comcast would like to test the hypothesis that the average monthly bill is higher than $ 86 this year. A random sample of 52 households was chosen. Assume the standard deviation of monthly cable bills in the country is $ 17.

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

b. Using σ = 0.01, compute the probability of a Type II error occurring if the actual average monthly cable bill is $ 92.

c. Using σ = 0.05, compute the probability of a Type II error occurring if the actual average monthly cable bill is $ 92.

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