1. HW 12 Key

2. 16:51 Banks frequently compete by adding special services that distinguish them from rivals. These services can be expensive to provide. The bank hopes to retain customers who keep high balances in accounts that do not pay large interest rates. Typical customers at this bank keep an average balance of $3,500 in savings accounts that pay 2% interest annually. The bank loans this money to other customers at an average rate of 6%, earning 4% profit on the balance. A sample of 65 customers was offered a special personalized account. After 3 months, the average balance in savings for these customers was $5,000 (s=$3,000). If the service costs the bank $50 per customer per year, is this going to be profitable to roll out on a larger scale?

3. 16:51 a a.State the null and alternative hypotheses. Describe the parameters. H0:mew 50; mew denotes the average increase in interest profit on a savings account when offered this service.

4. 16:51 b b. Describe Type I and Type II errors in this context. A Type I error implies that the bank rolled out the program, but it will not be profitable. A Type II error implies that the bank should have rolled it out (rejected H0) but did not.

5. 16:51 c c. What is necessary for the sample size to be adequate for using a t test? K must be less than 6.5 and the absolute kurtosis must be less than 6.5.

6. 16:51 d d. Find the p value of the test. Do the data supply enough evidence to reject the null hypothesis if alpha=.05? (Assume that the data meet the sample size condition.) The p value =P(T>.67)~.25. No.

7. 16:53 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. 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 a sale. For example, an order for $100 produces $20 in profit. Should the company agree to the asking price?

8. 16:53 a a.Why would a company want to run an experiment? Why not just buy the list and see what happens? The company doesn’t want to spend money on the names if it does not get a sufficient return on investment for it to be worth it.

9. 16:53 b b. Why would the holder of the list agree to allow the potential purchaser to run an experiment? The holder of the list is confident that the results will be favorable so that the company will end up buying the list. If the list holder doesn’t allow the company to experiment, then the list holder won’t make any money.

10. 16:53 c c. Why is a hypothetical test relevant in this situation? The company can test whether it will be worth it to buy the entire list. The sample can be representative of the entire list, so the test is relevant to the company’s decision.

11. 16:53 d d. Describe the appropriate hypotheses and type of test to use. Choose (and justify) an alpha level for the test. Be sure to check that this choice satisfies the necessary conditions. The null hypothesis is that the profit per name is less than or equal to 3 (the cost per name). The alternative is that the profit per name is greater than 3. Set alpha as.05. Kurtosis is 12, multiplied by 10 it is still less than n, 225, therefore it is fine, assuming the sample was random.

12. 16:53 e e. Summarize the results of the sample mailing. Use a histogram and appropriate numerical statistics. Severely right skewed (lots of outliers) with mean of 33.66

13. 16:53 f 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. P=.0021

14. 16:53 g g. Summarize the results of the test. Make a recommendation to the management of Performance Tires. The mean profit from the sample is significantly higher than the cost of $33.66 per name, therefore the company should buy the names.