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.Managerial ReportPrepare 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.CurrentNew263276260270266262271265257261282252257263265288258287269265262275263267283261262272259259282282254249271262265279267265269273286260288263279279271275274282264275259270277269274263280284273249272252262259274269266262278260273256275264261278Solve the questions given in the image attached using this data. Hypothesis TestConduct 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. LetM₁ = population mean driving distance for the current golf ball andM₂ = population mean driving distance for the new golf ball.State the null and alternative hypotheses. (Enter != for as needed.)Ho: Mì - 1250Ha: M1-M₂0Find the value of the test statistic. (Use μ₁ −μ₂. Round your answer to two decimal places.)0.88XFind the p-value. (Round your answer to four decimal places.).1921XUsing a = 0.05, state your conclusion.The null hypothesis will notDescriptive StatisticsFind 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.)MeanCurrent 269.275New267.45Confidence Intervalsbe rejected. There is notyd toyd toStandard deviation Standard error8.7539.868sufficient evidence to conclude that the population mean driving distance for the current golf ball is longer than that of the new golf ball.You may need to use the appropriate appendix table or technology to answer this question.Develop a 95% confidence interval for the population mean driving distance in yards of each model. (Round your answers to two decimal places.)CurrentNewydydDevelop a 95% confidence interval for the difference between the means of the two populations. Use current - new. (Round your answers to two decimal places.)-2.39Xyd to 6.04XydComment on the confidence intervals.The confidence intervals for the population mean driving distance overlap. The confidence interval for the difference between the means includesevidence to conclude that the mean driving distance for the current golf ball is longer than that of the new golf ball.zero. Thus, the result from the hypothesis test is confirmedby the confidence intervals. That is, there is insufficient ✓

Answered: Find the value of the test statistic.…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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.

Managerial Report

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
263	276
260	270
266	262
271	265
257	261
282	252
257	263
265	288
258	287
269	265
262	275
263	267
283	261
262	272
259	259
282	282
254	249
271	262
265	279
267	265
269	273
286	260
288	263
279	279
271	275
274	282
264	275
259	270
277	269
274	263
280	284
273	249
272	252
262	259
274	269
266	262
278	260
273	256
275	264
261	278

Solve the questions given in the image attached using this data.

Hypothesis Test
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
M₁ = population mean driving distance for the current golf ball and
M₂ = population mean driving distance for the new golf ball.
State the null and alternative hypotheses. (Enter != for as needed.)
Ho: Mì - 1250
Ha: M1-M₂0
Find the value of the test statistic. (Use μ₁ −μ₂. Round your answer to two decimal places.)
0.88
X
Find the p-value. (Round your answer to four decimal places.)
.1921
X
Using a = 0.05, state your conclusion.
The null hypothesis will not
Descriptive Statistics
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
Current 269.275
New
267.45
Confidence Intervals
be rejected. There is not
yd to
yd to
Standard deviation Standard error
8.753
9.868
sufficient evidence to conclude that the population mean driving distance for the current golf ball is longer than that of the new golf ball.
You may need to use the appropriate appendix table or technology to answer this question.
Develop a 95% confidence interval for the population mean driving distance in yards of each model. (Round your answers to two decimal places.)
Current
New
yd
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.)
-2.39
Xyd to 6.04
Xyd
Comment on the confidence intervals.
The confidence intervals for the population mean driving distance overlap
. The confidence interval for the difference between the means includes
evidence to conclude that the mean driving distance for the current golf ball is longer than that of the new golf ball.
zero. Thus, the result from the hypothesis test is confirmed
by the confidence intervals. That is, there is insufficient ✓

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Current	New
263	276
260	270
266	262
271	265
257	261
282	252
257	263
265	288
258	287
269	265
262	275
263	267
283	261
262	272
259	259
282	282
254	249
271	262
265	279
267	265
269	273
286	260
288	263
279	279
271	275
274	282
264	275
259	270
277	269
274	263
280	284
273	249
272	252
262	259
274	269
266	262
278	260
273	256
275	264
261	278

Current	New
263	276
260	270
266	262
271	265
257	261
282	252
257	263
265	288
258	287
269	265
262	275
263	267
283	261
262	272
259	259
282	282
254	249
271	262
265	279
267	265
269	273
286	260
288	263
279	279
271	275
274	282
264	275
259	270
277	269
274	263
280	284
273	249
272	252
262	259
274	269
266	262
278	260
273	256
275	264
261	278

Current	New
263	276
260	270
266	262
271	265
257	261
282	252
257	263
265	288
258	287
269	265
262	275
263	267
283	261
262	272
259	259
282	282
254	249
271	262
265	279
267	265
269	273
286	260
288	263
279	279
271	275
274	282
264	275
259	270
277	269
274	263
280	284
273	249
272	252
262	259
274	269
266	262
278	260
273	256
275	264
261	278