A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay $100 for the upgrade.

For the upgrade to be profitable, the company needs to sell it to more than 20% of their customers.

You contact a random sample of 60 customers and find that 16 would be willing to pay $100 for the upgrade.

(a) Do the sample data give good evidence that more than 20% of the company’s customers are willing to purchase the upgrade? Carry out an appropriate test at the a = 0.05 significance level.

(b) Which would be a more serious mistake in this setting—a Type I error or a Type II error? Justify your answer.

(c) Describe two ways to increase the power of the test in part (a).