Driven, a recently released magazine targeted to young professionals, states that 65% of its subscribers have an annual income greater than $100,000. The sales staff at Driven 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. Driven is currently trying to sell a large amount of advertising to Meuscher, an upscale chocolatier, for a special year-end issue on fine foods and wines. Before committing to advertise in Driven, Meuscher’s market research staff has decided to randomly sample 201 of Driven ’s subscribers to verify Driven ’s claim that 65% of its subscribers earn more than $100,000 annually.
a. The file Driven 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 Driven 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 Meuscher advertise in Driven?