Par, Inc., is a major manufacturer of golf equipment. Management believes that Par's market share could be increased with the introduction of a cut-resistant, longer-lasting golf ball. Therefore, the research group at Par has been investigating a new golf ball coating designed 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 driving distances. Par would like the new cut-resistant ball to offer driving distances comparable to those of the current-model golf ball. To compare the driving distances for the two balls, 40 balls of both the new and current models were subjected to distance tests. The testing was performed with a mechanical hitting machine so that any difference between the mean distances for the two models could be attributed to a difference in the two models. Prepare a managerial report that investigates the effect of the new coating on driving distances of golf balls by comparing driving distances for the two models. Consider the results of the tests, with distances measured to the nearest yard, in the complete data set. Current New 262 276 259 268 265 264 270 265 256 263 281 252 256 261 264 290 257 285 268 263 261 273 262 267 282 263 261 270 258 261 281 280 253 249 270 262 264 279 266 265 268 273 285 260 287 263 278 279 270 273 273 282 263 275 258 268 276 267 273 263 279 282 272 251 271 252 261 261 273 269 265 264 277 262 272 256 274 264 260 278 Conduct a hypothesis test that Par could use to compare the driving distances of the current and new golf balls. (You may need to use the appropriate appendix table or technology to answer this question.) Formulate hypotheses that can be used to determine whether the sample data support the hypothesis that the population mean driving distance for the current golf ball is longer than that of the new golf ball. Let ?1 = population mean driving distance for the current golf ball and ?2 = population mean driving distance for the new golf ball. State the null and alternative hypotheses. (Enter != for ≠ as needed.) H0: μ1−μ2=0 Ha: μ1−μ2>0 Find the value of the test statistic. (Use ?1 − ?2. Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) Find the mean, standard deviation, and standard error for the driving distance (in yards) for current and new models of golf balls. (Round your answers to three decimal places.) Mean Standard deviation Standard error Current New Develop a 95% confidence interval for the population mean driving distance in yards of each model. (Round your answers to two decimal places.) Current yd to ydNew yd to yd Develop a 95% confidence interval for the difference between the means of the two populations. Use current − new. (Round your answers to two decimal places.) yd to yd Comment on the confidence intervals. The confidence intervals for the population mean driving distance . The confidence interval for the difference between the means zero. Thus, the result from the hypothesis test is by the confidence intervals. That is, there is evidence to conclude that the mean driving distance for the current golf ball is longer than that of the new golf ball.

Par, Inc., is a major manufacturer of golf equipment. Management believes that Par's market share could be increased with the introduction of a cut-resistant, longer-lasting golf ball. Therefore, the research group at Par has been investigating a new golf ball coating designed 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 driving distances. Par would like the new cut-resistant ball to offer driving distances comparable to those of the current-model golf ball. To compare the driving distances for the two balls, 40 balls of both the new and current models were subjected to distance tests. The testing was performed with a mechanical hitting machine so that any difference between the mean distances for the two models could be attributed to a difference in the two models. Prepare a managerial report that investigates the effect of the new coating on driving distances of golf balls by comparing driving distances for the two models. Consider the results of the tests, with distances measured to the nearest yard, in the complete data set. Current New 262 276 259 268 265 264 270 265 256 263 281 252 256 261 264 290 257 285 268 263 261 273 262 267 282 263 261 270 258 261 281 280 253 249 270 262 264 279 266 265 268 273 285 260 287 263 278 279 270 273 273 282 263 275 258 268 276 267 273 263 279 282 272 251 271 252 261 261 273 269 265 264 277 262 272 256 274 264 260 278 Conduct a hypothesis test that Par could use to compare the driving distances of the current and new golf balls. (You may need to use the appropriate appendix table or technology to answer this question.) Formulate hypotheses that can be used to determine whether the sample data support the hypothesis that the population mean driving distance for the current golf ball is longer than that of the new golf ball. Let ?1 = population mean driving distance for the current golf ball and ?2 = population mean driving distance for the new golf ball. State the null and alternative hypotheses. (Enter != for ≠ as needed.) H0: μ1−μ2=0 Ha: μ1−μ2>0 Find the value of the test statistic. (Use ?1 − ?2. Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) Find the mean, standard deviation, and standard error for the driving distance (in yards) for current and new models of golf balls. (Round your answers to three decimal places.) Mean Standard deviation Standard error Current New Develop a 95% confidence interval for the population mean driving distance in yards of each model. (Round your answers to two decimal places.) Current yd to ydNew yd to yd Develop a 95% confidence interval for the difference between the means of the two populations. Use current − new. (Round your answers to two decimal places.) yd to yd Comment on the confidence intervals. The confidence intervals for the population mean driving distance . The confidence interval for the difference between the means zero. Thus, the result from the hypothesis test is by the confidence intervals. That is, there is evidence to conclude that the mean driving distance for the current golf ball is longer than that of the new golf ball.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter4: Linear Functions

Section: Chapter Questions

Problem 8PT: Does Table 1 represent a linear function? If so, finda linear equation that models the data.

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Question

One of the researchers voiced concern about the effect of the new coating on driving distances. Par would like the new cut-resistant ball to offer driving distances comparable to those of the current-model golf ball. To compare the driving distances for the two balls, 40 balls of both the new and current models were subjected to distance tests. The testing was performed with a mechanical hitting machine so that any difference between the mean distances for the two models could be attributed to a difference in the two models.

Prepare a managerial report that investigates the effect of the new coating on driving distances of golf balls by comparing driving distances for the two models.

Consider the results of the tests, with distances measured to the nearest yard, in the complete data set.

Current	New
262	276
259	268
265	264
270	265
256	263
281	252
256	261
264	290
257	285
268	263
261	273
262	267
282	263
261	270
258	261
281	280
253	249
270	262
264	279
266	265
268	273
285	260
287	263
278	279
270	273
273	282
263	275
258	268
276	267
273	263
279	282
272	251
271	252
261	261
273	269
265	264
277	262
272	256
274	264
260	278

Conduct a hypothesis test that Par could use to compare the driving distances of the current and new golf balls. (You may need to use the appropriate appendix table or technology to answer this question.)

Formulate hypotheses that can be used to determine whether the sample data support the hypothesis that the population mean driving distance for the current golf ball is longer than that of the new golf ball. Let

?₁ = population mean driving distance for the current golf ball

and

?₂ = population mean driving distance for the new golf ball.

State the null and alternative hypotheses. (Enter != for ≠ as needed.)

H₀:

μ1−μ2=0

H_a:

μ1−μ2>0

Find the value of the test statistic. (Use

?₁ − ?₂.

Round your answer to two decimal places.)

Find the p-value. (Round your answer to four decimal places.)

Find the mean, standard deviation, and standard error for the driving distance (in yards) for current and new models of golf balls. (Round your answers to three decimal places.)

	Mean	Standard deviation	Standard error
Current
New

Develop a 95% confidence interval for the population mean driving distance in yards of each model. (Round your answers to two decimal places.)

Current yd to ydNew yd to yd

Develop a 95% confidence interval for the difference between the means of the two populations. Use current − new. (Round your answers to two decimal places.)

yd to yd

Comment on the confidence intervals.

The confidence intervals for the population mean driving distance . The confidence interval for the difference between the means zero. Thus, the result from the hypothesis test is by the confidence intervals. That is, there is evidence to conclude that the mean driving distance for the current golf ball is longer than that of the new golf ball.

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Current	New
262	276
259	268
265	264
270	265
256	263
281	252
256	261
264	290
257	285
268	263
261	273
262	267
282	263
261	270
258	261
281	280
253	249
270	262
264	279
266	265
268	273
285	260
287	263
278	279
270	273
273	282
263	275
258	268
276	267
273	263
279	282
272	251
271	252
261	261
273	269
265	264
277	262
272	256
274	264
260	278

Current	New
262	276
259	268
265	264
270	265
256	263
281	252
256	261
264	290
257	285
268	263
261	273
262	267
282	263
261	270
258	261
281	280
253	249
270	262
264	279
266	265
268	273
285	260
287	263
278	279
270	273
273	282
263	275
258	268
276	267
273	263
279	282
272	251
271	252
261	261
273	269
265	264
277	262
272	256
274	264
260	278

Current	New
262	276
259	268
265	264
270	265
256	263
281	252
256	261
264	290
257	285
268	263
261	273
262	267
282	263
261	270
258	261
281	280
253	249
270	262
264	279
266	265
268	273
285	260
287	263
278	279
270	273
273	282
263	275
258	268
276	267
273	263
279	282
272	251
271	252
261	261
273	269
265	264
277	262
272	256
274	264
260	278