Statistics Homework Help

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?

This question relates to 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?

C) Why is it important that the 225 names be randomly selected from the list?

D) How is the certainty of your decision dependent on the number of names in the sample list? How would, for example, doubling the number of sample names change the certainty of your decision?

HINT: Look at the formulas for t.

This question relates to Method.

A) The first task is to form a hypothesis about the benefit of buying the list. In order to buy the list, we must believe that the investment will be worth the payout. 

Consider the cost of each name ($3), and the expected benefit for each name.  Note the expected benefit is NOT the same as the expected revenue in this example.  You will need to consider the profit margin on income to get the benefit.

You can write an equation for the breakeven revenue, per customer, to make buying the entire list a “go”.  The equation should be of the form:  Benefit – Cost > 0. 

What is the break-even average order size?  In other words, what is the dollar amount of an order that breaks even at a cost of $3 per order?

B) Why is a hypothesis test relevant in this situation?

C) Describe the appropriate hypotheses and type of test to use. Choose (and justify) an α-level for the test. Be sure to check that this choice satisfies the necessary conditions.

This question relates to Mechanics.

The histograms you need to answer this question have been provided for you in the exercise guide. However, if you’d like to use Python to manipulate the data or create these histograms on your own, check out the Jupyter Notebook Sandbox on the following Canvas Page.

A) Does the Spending per Order for All Orders (the green data) appear to be normally distributed?

B) Test the null hypothesis and report a p-value. If examination of the data suggest problems with the proposed plan for testing the null hypothesis, revise the analysis appropriately.

This question relates to Message.

A) 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).

B) If this were your company, and you made the decision to buy the list and lost money on the deal, how would you respond to criticism of your decision?