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.

1. 
   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?

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