3The overall distance traveled by a golf ball is tested by h

3.The overall distance traveled by a golf ball is tested by hitting the ball with Iron Byron, a mechanical golfer with a swing that is said to emulate the distance hit by the legendary champion, Byron Nelson. Ten randomly selected balls of two different brands are tested and the overall distance measured. The data are given below: Brand1 275 286 287 271 283 271279 2 275 2 263 267 n, 10 - = 275.7 s 8.0284 Brand2 258 244 260 265 273 281 271 270 263 268 n2- 10 = 265.3 S210.0449 (a) Normal probability plots of the two data sets are given below. Results of the Shapiro-Wilk test (discussed Oct 12 R demo, see BlackBoard) of Normality are also given below. Are we justified in assuming that the two data sets come from Normal populations? Explain briefly and use some (you do not have to use all) of the results below to support your answer R commands (in bold) Brand1-c(275,286,287,271,283,271,279,275,263,267) Brand2-c(258,244,260,265,273,281,271,270,263,268) qqnorm(Brand1) qqnorm(Brand2) Brand 1 Brand 2 shapiro.test(Brand1) Shapiro-Wilk normality test data: Brand1 w = 0.958, p-value = 0.7629 shapiro.test(Brand2) Shapiro-Wilk normality test data: Brand2 W = 0.9583, p-value = 0.7663 Problem 3 is continued on the next page 15 05 05 15 15 05 05 15 Theorebcal Quantiles Theoretical Quantiies

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