This is everything i have so far in the excel sheet. I\'m stuck on how to comput

Question

This is everything i have so far in the excel sheet. I'm stuck on how to compute the confidence interval and why my p-value is higher than my alpha of 0.05.

Par, Inc., manufactures 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 investigates a new golf ball coating designed to resist cuts and provide a more durable ball. The tests with the coating show promising results

One of the researchers, Bill 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 the 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 design. The results of the tests, with distances measured to the nearest yard, follow. These data are available in the data set Golf.

The CEO tells you (in contrast to what Bill said) that he would like to sell the new ball unless there is overwhelming evidence that the cut-resistant ball is slower than the old ball so you should frame your hypothesis accordingly. Ten million dollars has already been spent on the new ball and the future of the company could be at stake. Hint: you are more willing to make a Type II error: Analyze the data to provide the hypothesis testing conclusion and statements (at .05). Use one of the formats hypothesis formats or the appropriate format from your textbook (can use H1 and H2). Use the following notations for your population values: m1 are the old golf balls and m2 are the new ones.

Samples Current (x) New (y) (x-x(mean)^2 (y-y(mean)^2) 1 264.00 277.00 39.375625 90.25 STD. DEV 9.3875675 2 261.00 269.00 86.025625 2.25 3 267.00 263.00 10.725625 20.25 4 272.00 266.00 2.975625 2.25 z-Test: Two Sample for Means 5 258.00 262.00 150.675625 30.25 6 283.00 251.00 161.925625 272.25 264 277 7 258.00 262.00 150.675625 30.25 Mean 270.435897 267.2564103 8 266.00 289.00 18.275625 462.25 Known Variance 77.5681511 98.0904184 9 259.00 286.00 127.125625 342.25 Observations 39 39 10 270.00 264.00 0.075625 12.25 Hypothesized Mean Difference 0 11 263.00 274.00 52.925625 42.25 z 1.49814797 12 264.00 266.00 39.375625 2.25 P(Z<=z) one-tail 0.0670474 13 284.00 262.00 188.375625 30.25 z Critical one-tail 1.64485363 14 263.00 271.00 52.925625 12.25 P(Z<=z) two-tail 0.13409481 15 260.00 260.00 105.575625 56.25 z Critical two-tail 1.95996398 16 283.00 281.00 161.925625 182.25 17 255.00 250.00 233.325625 306.25 18 272.00 263.00 2.975625 20.25 CURRENT 277 19 266.00 278.00 18.275625 110.25 20 268.00 264.00 5.175625 12.25 Mean 270.435897 Mean 267.25641 21 270.00 272.00 0.075625 20.25 Standard Error 1.41029322 Standard Error 1.58591896 22 287.00 259.00 279.725625 72.25 Median 270 Median 264 23 289.00 264.00 350.625625 12.25 Mode 272 Mode 263 24 280.00 280.00 94.575625 156.25 Standard Deviation 8.80727831 Standard Deviation 9.9040607 25 272.00 274.00 2.975625 42.25 Sample Variance 77.5681511 Sample Variance 98.0904184 26 275.00 281.00 22.325625 182.25 Kurtosis -0.78776409 Kurtosis -0.44396285 27 265.00 276.00 27.825625 72.25 Skewness 0.26112481 Skewness 0.29922934 28 260.00 269.00 105.575625 2.25 Range 34 Range 39 29 278.00 268.00 59.675625 0.25 Minimum 255 Minimum 250 30 275.00 262.00 22.325625 30.25 Maximum 289 Maximum 289 31 281.00 283.00 115.025625 240.25 Sum 10547 Sum 10423 32 274.00 250.00 13.875625 306.25 Count 39 Count 39 33 273.00 253.00 7.425625 210.25 Largest(1) 289 Largest(1) 289 34 263.00 260.00 52.925625 56.25 Smallest(1) 255 Smallest(1) 250 35 275.00 270.00 22.325625 6.25 Confidence Level(95.0%) 2.85498935 Confidence Level(95.0%) 3.21052508 36 267.00 263.00 10.725625 20.25 SUMMARY OUTPUT 37 279.00 261.00 76.125625 42.25 38 274.00 255.00 13.875625 156.25 SUMMARY OUTPUT 39 276.00 263.00 32.775625 20.25 40 262.00 279.00 68.475625 132.25 Regression Statistics totals 10811.00 10700.00 Multiple R 0.06587679 Mean 270.28 267.50 R Square 0.00433975 Adjusted R Square -0.02256998 Standard Error 10.0152043 Observations 39 ANOVA df SS MS F Significance F Regression 1 16.17614588 16.1761459 0.16127068 0.69029951 Residual 37 3711.259752 100.304318 Total 38 3727.435897 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 287.290442 49.91314338 5.75580743 1.3448E-06 186.156807 388.424076 186.156807 388.424076 264 -0.07408052 0.184470233 -0.40158521 0.69029951 -0.44785271 0.29969168 -0.44785271 0.29969168

Explanation / Answer

how to compute the confidence interval

The 95% confidence interval for the difference in the means of x's and y's is (-1.384, 6.934)

and why my p-value is higher than my alpha of 0.05

The p-value being higher than the alpha of 0.05 means that the mean difference is insignificant and that the mean x's and y's are equal.

Regression analysis and ANOVA do not seem appropriate for the problem on hand at all. The reason is that the tests are carried out on entirely different balls and there is now relation between the new and old balls to carry out the correlation study such as regression analysis and ANOVA.

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