Discussion:
Scenario 1
The manager of the Gander Mountain store in Frogtown, IL, believes that his prices for ammunition are lower than the prices of his primary competitor in the hunting equipment market, Cabela's. He would like to be able to provide evidence to support this assertion.
- What are the Gander Mountain manager's null and alternative hypotheses?
- How should he go about taking samples to gather data for testing the hypotheses?
- What statistical test should he use to test his hypothesis, using the data he has collected?
Scenario 2
A major manufacturer of golf equipment seeks to improve its market share by introducing a golf ball that is less likely to slice when hit. The company's research and development group has been experimenting with dimple patterns that promote straight flight, and have achieved some degree of success. The vice president of marketing, however, is worried about the effect that the new pattern might have on driving distance.
"I do not care how slice-resistant this ball is, if it does not go as far as the old one, no one is going to buy it. Telling a golfer to buy some ball that cannot be driven as far as the old one is a complete non-starter," he commented to the development project manager.
To investigate this issue, the research and development group did a test to compare the driving distances for the two balls: 50 balls of the new type, and 50 of the old. They used a mechanical hitting machine to control all factors other than the balls themselves. The resulting data of distance measured to the nearest yard for each of the 100 balls that were hit is provided in the Golf Ball Distance Test Excel file.
- What is the null hypothesis that the research and development group is testing?
- Analyze the data
- What is the appropriate statistical test for determining the null hypothesis?
- What is the p-value?
- What should you tell the vice president of marketing?
| Golf Ball Distance Test |
| Distance Measured in Yards |
| Current |
New |
| 264 |
277 |
| 261 |
269 |
| 267 |
263 |
| 272 |
266 |
| 258 |
262 |
| 283 |
251 |
| 258 |
262 |
| 266 |
289 |
| 259 |
286 |
| 270 |
264 |
| 263 |
274 |
| 264 |
266 |
| 284 |
262 |
| 263 |
271 |
| 260 |
260 |
| 283 |
281 |
| 255 |
250 |
| 272 |
263 |
| 266 |
278 |
| 268 |
264 |
| 270 |
272 |
| 287 |
259 |
| 289 |
264 |
| 280 |
280 |
| 272 |
274 |
| 275 |
281 |
| 265 |
276 |
| 260 |
269 |
| 278 |
268 |
| 275 |
262 |
| 281 |
283 |
| 274 |
250 |
| 273 |
253 |
| 263 |
260 |
| 275 |
270 |
| 267 |
263 |
| 279 |
261 |
| 274 |
255 |
| 276 |
263 |
| 262 |
279 |