Suppose the United States Golf Association wants to compare the distances associ

Question

Suppose the United States Golf Association wants to compare the distances associated with four different brands of golf clubs when struck with a driver. Iron Byron, the USGA’s robotic golfer, is used to hit a random sample of ten balls of each brand in a random sequence. The distance is recorded for each hit, and the results are shown below.

*Analyze the data using a=.05. Perform multiple comparisons if necessary.

Brand A

Brand B

Brand C

Brand D

251.2

263.2

269.7

251.6

245.1

262.9

263.2

248.6

248.0

265.0

277.5

249.4

251.1

254.5

267.4

242.0

265.5

264.3

270.5

246.5

250.0

257.0

265.5

251.3

253.9

262.8

270.7

262.8

244.6

264.4

272.9

249.0

254.6

260.9

275.6

247.1

248.8

255.9

266.5

245.9

Brand A

Brand B

Brand C

Brand D

251.2

263.2

269.7

251.6

245.1

262.9

263.2

248.6

248.0

265.0

277.5

249.4

251.1

254.5

267.4

242.0

265.5

264.3

270.5

246.5

250.0

257.0

265.5

251.3

253.9

262.8

270.7

262.8

244.6

264.4

272.9

249.0

254.6

260.9

275.6

247.1

248.8

255.9

266.5

245.9

Explanation / Answer

Using ANOVA, we can analysis this

The p-value is less than 0.05. We conclude that their is means distances different with four different brands of golf clubs when struck with a driver.

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Column 1 10 2512.8 251.28 35.72178 Column 2 10 2610.9 261.09 14.92544 Column 3 10 2699.5 269.95 20.25833 Column 4 10 2494.2 249.42 29.94622 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 2711.085 3 903.695 35.8425 6.59E-11 2.866266 Within Groups 907.666 36 25.21294 Total 3618.751 39

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