Question: 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 significance level.

(b) Describe a Type I and a Type II error in the context of this problem. Which would be the more serious mistake in this setting and why?