A popular magazine aimed at IT professionals states that 65% of its subscribers have an annual income greater than $100,000. The magazine’s staff uses this high proportion of subscribers earning more than

$100,000 as a selling point when trying to get companies to place advertisements with the magazine.

Before committing to advertise in this magazine, a computer hardware firm’s market research staff has decided to randomly sample 196 subscribers to verify the claim that 65% of its subscribers earn more than $100,000 annually.

a. The file High Tech contains the responses of 196 randomly sampled subscribers of the magazine. The responses are coded “Yes” if the subscriber earns more than $100,000 annually and “No” if the subscriber does not earn more than $100,000 annually. Open the file and create a new variable that has a value of 1 for “Yes” and 0 for “No.”

b. Calculate the sample proportion of subscribers who have annual incomes greater than $100,000.

c. How likely is it that a sample proportion greater than the one calculated in part b would be obtained if the population proportion of subscribers earning more than $100,000 annually is 65%?

d. Based on the probability you calculated in part

c, should the hardware firm advertise in this magazine?