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Hypothesis testing problems for Callaway Golf Company

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1. Callaway Golf Company's new forged titanium ERC driver has been described as "illegal" because it promises driving distances that exceed the USGA's standard. Golf Digest compared actual driving distances with the ERC driver and a USGA approved driver with a population mean driving distance of 280 yards. Based on nine test drives, the mean driving distance by the ERC driver was 286.9 yards (Golf Digest, May 12, 2000). Answer the following questions assuming a sample standard deviation driving distance of 10 yards.

a. Formulate the null and alternate hypotheses that can be used to determine whether the new ERC driver has a population mean driving distance greater than 280 yards.
b. On average, how many yards farther did the golf ball travel with the ERC driver?
c. At α = 0.05, what is your conclusion?

2. Microsoft Outlook is the most widely used e-mail manager. A Microsoft executive claims that Microsoft Outlook is used by at least 75% of the Internet users. A sample of Internet users will be used to test this claim.

a. Formulate the hypotheses that can be used to test the claim.
b. A Merrill Lynch study reported that Microsoft Outlook is used by 72% of Internet users (CNBC, June 2000). Assume that the report was based on a sample size of 300 Internet users. What is the p-value?
c. At α = 0.05, should the executive's claim of at least 75% be rejected?

3. An extensive study of the cost of health care in the United States presented data showing that the mean spending per Medicare enrollee was $6883. To investigate differences across the country, a researcher took a sample of 40 Medicare enrollees in Indianapolis. For the Indianapolis sample, the mean 2003 Medicare spending was $5980 and the standard deviation was $2518.

a. State the hypothesis for deter ming whether the mean annual Medicare spending in Indianapolis is lower than the national mean.
b. Use the preceding sample results to compute the test statistic and the p value.
c. Use a=.05(level of significance). What is your conclusion?
d. Repeat the hypothesis test using the critical value approach.

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Solution Summary

Step by step method for testing the hypothesis under 5 step approach is discussed here. Excel template for each problem is also included. This template can be used to obtain the answers of similar problems.

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Mean Driving Distance

Callaway Golf is one of the leading golf equipment manufacturers in the United States. The company's R&D department has created three new golf ball designs (GB1, GB2 and GB3) that result in reduced air drag and thereby increase driving distance. The company currently has three distinct brands of driver clubs: FX1, FX2 and FX3. Callaway must decide which golf ball design and driver brand pair to promote in a joint promotional campaign. Callaway executives think that whichever pair (golf ball design + Driver brand) leads to the greatest driving distance would be the better choice. Callaway randomly and independently assigns 4 professional golfers to each of the 9 golf ball design â?" driver brand combinations. The driving distance of each golfer is then recorded and stored in the file balldesign.sav. Does the mean driving distance differ for the three golf ball designs? Does the mean driving distance differ for the three driver brands? Does the driver brand affect the mean driving distance of the golf ball deign?

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