A sporting goods manufacturing company wanted to compare the distance traveled by golf balls produced using four different designs. Ten balls were manufactured with each design and were brought to the local golf course for the club professional to test. The order in which the balls were hit with the same club from the first tee was randomized so that the pro did not know which type of ball was being hit. All 40 balls were hit in a short period of time, during which the environmental conditions were essentially the same. The results (distance traveled in yards) for the four designs are stored in Golf ball and shown in the following table:

a. At the 0.05 level of significance, is there evidence of a difference in the mean distances traveled by the golf balls with different designs?
b. If the results in (a) indicate that it is appropriate to do so, use the Tukey-Kramer procedure to determine which designs differ in mean distances.
c. What assumptions are necessary in (a)?
d. At the 0.05 level of significance, is there evidence of a difference in the variation of the distances traveled by the golf balls with different designs?
e. What golf ball design should the manufacturing manager choose? Explain.

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Design 2 217.08 221.43 218.04 224.13 211.82 Design 3 226.77 224.79 229.75 228.51 221.44 223.85 223.97 234.30 219.50 233.00 Design 1 206.32 Design 4 230.55 227.95 206-19 204.45 209.65 203.81 206.75 205.68 204.49 210.86 224.87 229.49 231.10 221.53 235.45 228.35 225.09 221.28 229.43 214.51