1. Stine and Foster: Hypothesis Testing
Chapter 16 Problems
Stine and Foster: Hypothesis Testing

2. Problem 40: Electric Components
The electronic components used to assemble a cellular phone have been exceptionally reliable, with more than 99.9% working correctly. The head of procurement believes that the current supplier meets this standard, but he tests components just the same. A test of a sample of 100 components yielded no defects. Do these data prove beyond reasonable doubt that the components continue to exceed the 99.9% target.

3. Questions
Identify the relevant population parameter and null hypothesis.
Explain why it is not appropriate to use a normal approximation for the sampling distribution of the proportion in this situation.
Determine if the data supply enough evidence to reject the null hypothesis. Identify any assumptions you need for the calculation.

4. Problem 41: Supermarket Shelves
A company that stocks shelves in supermarkets is considering expanding the supply that it delivers. Items that are not sold must be discarded at the end of the day, so it only wants to schedule additional deliveries if stores regularly sell out. A break-even analysis indicates that an additional delivery cycle will be profitable if items are selling out in more than 60% of markets. A survey during the last week in 45 markets found the shelves bare in 35.

5. Questions State the null and alternative hypotheses.
Describe a Type I error and a Type II error in this context.
Find the p-value of the test. Do the data supply enough evidence to reject the null hypothesis if the a-level is 0.05?

6. Problem 42: Sports Drink
Field tests of a low-calorie sport drink found that 80 of the 100 who tasted the beverage preferred it to the regular higher-calorie drink. A break-even analysis indicates that the launch of this product will be profitable if the beverage is preferred by more than 75% of all customers.

7. Questions State the null and alternative hypotheses.
Describe a Type I error and a Type II error in this context.
Find the p-value for a test of the null hypothesis. If a = 0.10, does the test reject H0?

8. Problem 43: Hotel Chain
The management of a chain of hotels avoids intervening in the local management of its franchises unless problems become far too common to ignore. Management believes that solving the problems is better left to the local staff unless the measure of satisfaction drops below 33%. A survey of 80 guests who recently stayed in the franchise in St. Louis found that only 20% of the guests indicated that they would return to that hotel when next visiting the city. Should management intervene in the franchise in St. Louis?

9. Questions State the null and alternative hypotheses.
Describe Type I and Type II errors in this context.
Find the p-value of the test. Do the data supply enough evidence to reject the null hypothesis if a = 0.025?

10. Problem 44: Importer
An importer of electronic goods is considering packaging a new, easy-to-read instruction booklet with DVD players. It wants to package this booklet only if it helps customers more than the current booklet. Previous tests found that only 30% of customers were able to program their DVD player. An experiment with the new booklet found that 16 out of 60 customers were able to program their DVD player.

11. Questions State the null and alternative hypotheses.
Describe Type I and Type II errors in this context.
Find the p-value of the test. Do the data supply enough evidence to reject the null hypothesis if a = 0.05?

12. Problem 45: Loyalty Programs
A variety of stores offer loyalty programs. Participat- ing shoppers swipe a bar-coded tag at the register when checking out and receive discounts on certain purchases. Stores benefit by gleaning information about shopping habits and hope to encourage shoppers to spend more. A typical Saturday morning shopper who does not participate in this program spends $120 on her or his order. In a sample of 80 shoppers participating in the loyalty program, each shopper spent $130 on average during a recent Saturday, with standard deviation s = +40. (see the histogram on the next page.) Is this statistical proof that the shoppers participating in the loyalty program spend more on average than typical shoppers? (Assume that the data meet the sample size condition.

13. Histogram

14. Questions
State the null and alternative hypotheses. Describe the parameters.
Describe the Type I and Type II errors.
How large could the kurtosis be without violating the CLT condition?
Find the p-value of the test. Do the data supply enough evidence to reject the null hypothesis if a = 0.05?

15. Problem 46: Cadillac
Brand managers become concerned if they discover that customers are aging and gradually moving out of the high-spending age groups. For example, the average Cadillac buyer is older than 60, past the prime middle years that typically are associated with more spending. Part of the importance to Cadillac of the success of the Escalade model has been its ability to draw in younger customers. If a sample of 50 Escalade purchasers has average age 45 (with standard deviation 25), is this compelling evidence that Escalade buyers are younger on average than the typical Cadillac buyer? (Assume that the data meet the sample size condition.)

16. Problem 47 Refer to the analysis of shoppers in Exercise 45.
If several of those participating in the loyalty program are members of the same family, would this cause you to question the assumptions that underlie the test in this question?
Several outliers were observed in the data for the loyalty program. Should these high-volume purchases be excluded?