Suppose the average operating time per charge for a 6 volt laptop battery is currently 4.0 hours. Let’s say SWET Electronic Technology claims it has developed a new 6 volt battery that has an average charge life that exceeds 4.0 hours. To test the effectiveness of this new technology, a random sample of 45 batteries was selected and the operating time per charge for each battery was recorded. Assume the standard deviation is 0.7 hours.

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

b. Using σ = 0.05, calculate the probability of a Type II error occurring if the average operating time per charge is actually 4.4 hours.

c. Using σ = 0.01, calculate the probability of a Type II error occurring if the average operating time per charge is actually 4.4 hours.

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