Performance Tires plans to engage in direct mail advertising. It is currently in negotiations to purchase a mailing list of the names of people who bought sports cars within the last three years. The owner of the mailing list claims that sales generated by contacting names on the list will more than pay for the cost of using the list. (Typically, a company will not sell its list of contacts, but rather provides the mailing services. For example, the owner of the list would handle addressing and mailing catalogs.)
Before it is willing to pay the asking price of $3 per name, the company obtains a sample of 225 names and addresses from the list in order to run a small experiment. It sends a promotional mailing to each of these customers. The data for this exercise show the gross dollar value of the orders produced by this experimental mailing. The company makes a profit of 20% of the gross dollar value of a sale. For example, an order for $100 produces $20 in profit. Should the company agree to the asking price?
Motivation
(a) Why would a company want to run an experiment? Why not just buy the list and see what happens?
(b) Why would the holder of the list agree to allow the potential purchaser to run an experiment?
Method
(c) Why is a hypothesis test relevant in this situation?
(d) Describe the appropriate hypotheses and type of test to use. Choose (and justify) an a-level for the test. Be sure to check that this choice satisfies the necessary conditions.
Mechanics
(e) Summarize the results of the sample mailing. Use a histogram and appropriate numerical statistics.
(f) Test the null hypothesis and report a p-value. If examination of the data suggests problems with the proposed plan for testing the null hypothesis, revise the analysis appropriately.
Message
(g) Summarize the results of the test. Make a recommendation to the management of Performance Tires (avoid statistical jargon, but report the results of the test).