Case Problem: GOLF, LTD. GOLF LTD., is one of the manufacturers of golf equipment in Canada. The senior management believes that GOLF's market share could be increased with the introduction of a cut-resistant, longer lasting golf ball. Therefore, the research group at GOLF has been investigating a new golf ball coating to resist cuts and provide a more durable ball. The tests with the coating have been promising. One of the researchers voiced concern about the effect of the new coating on the driving distance of the balls. GOLF would like the new cut-resistant balls to offer driving distances compatible to those of the current model golf balls. To compare the driving distances for the two balls, 40 balls of both the new and current model balls were subjected to distance tests. The testing was performed with a mechanical hitting machine so that any difference between the mean differences between the two models could be attributed to a difference in the two models. The results of the tests, with distances measured to the nearest yard are shown in the following table. Model Model Model Model Current New Current New Current New Current New 264 277 270 272 263 274 281 283 261 269 287 259 264 266 274 250 267 263 289 264 284 262 273 253 272 266 280 280 263 271 263 260 258 262 272 274 260 260 275 270 283 251 275 281 283 281 267 263 258 262 265 270 255 250 279 261 266 289 260 269 272 263 274 255 259 286 278 268 266 278 276 263 270 264 275 262 268 264 262 279 1. Formulate and present the rational for a hypothesis test that Golf could use to compare the driving distance of the current and new golf balls. 2. Analyze the data to provide the hypothesis testing conclusion. What is the p-value for your test? What is your recommendation for GOLF LTD.? 3. Provide a descriptive statistical summary of the data for each model. 4. Do you see a need for larger sample sizes and more testing with the golf balls? Discuss. To answer the above questions and write a managerial report, please note that the case relates to comparing two populations' means. A/B testing is the concept that relates to this case. Watch "Data Science in Minutes" Video on week 6 of the course page to learn about A/B testing. Formulate the hypothesis that there is no difference between the mean driving distance of the two balls (current and new) and use paired t tests (matched samples) to test the hypothesis. You can use Excel's data analysis tool pack and run the t test.