Question

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. Use the data provided to answer the following questions: 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? 3. If the golf ball manufacturer wished to build the golf ball with the greatest distance, which design should the firm select?

	A	B	C	D
1	221.84	244.90	247.89	233.40
2	223.58	241.69	245.09	238.08
3	221.70	247.03	249.27	234.44
4	219.82	245.69	241.78	240.98
5	225.42	238.09	246.75	227.75
6	219.14	240.68	248.48	229.99
7	222.30	240.81	238.19	237.92
8	221.15	251.92	253.16	246.68
9	219.87	236.01	245.52	229.60
10	226.72	250.52	242.02	230.64
11	240.39	259.87	263.52	255.99
12	236.36	264.17	259.96	259.11
13	235.62	258.78	267.16	247.28
14	237.78	270.86	272.19	265.23
15	243.77	269.36	260.22	247.99

Answer 1

Part 1: -

A one way ANOVA was applied to check if there is any significant difference in the mean distances traveled by the golf balls with different designs.

Null Hypothesis : u₁ = u₂ = u₃ = u₄

Alternate Hypothesis : Not all the means are equal

The data points were analysed in Excel and the output of ANOVA (single factor) is shown below: -

From the output it can be analysed that P value is less than 0.05, hence Null Hypothesis should be rejected.

Hence, it can be concluded that there is a significance difference in the mean distances traveled by the golf balls with different designs.