A golf ball manufacturer desires to compare the distance traveled by golf balls using four unique designs. Fifteen balls were manufactured and each was brought to the local golf course for testing by the local pro. The order of the golf balls hit by the professional was randomized so the pro did not know which ball was being hit. All 60 balls were hit over a short time period to reduce any potential environmental effects. Distances traveled for each ball are linked here (xlsx).
1. 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?
2. Do the results in question 1 indicate that it is appropriate to use the Tukey-Kramer procedure to determine which designs differ in mean distances? You may need to do a little research of your own to get the equations to do this...it is not hard but Excel does not do this calculation with a "couple of clicks."
3. If the golf ball manufacturer wished to build the golf ball with the greatest distance, which design should the firm select?