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.

	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

Use the data linked above to answer the following questions:

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?

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?

If the golf ball manufacturer wished to build the golf ball with the greatest distance, which design should the firm select?

Answer 1

Answer:

Use the data linked above to answer the following questions:

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?

Calculated F= 17.073, P=0.0000 which is < 0.05 level of significance. Ho is rejected. There is enough evidence of a difference in the mean distances traveled by the golf balls with different designs.

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?

Design A is significant with B, C and D.

Design C is significant with D.

If the golf ball manufacturer wished to build the golf ball with the greatest distance, which design should the firm select?

Design C.

Excel Addon PHStat used.

ANOVA: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
A	15	3415.46	227.6973333	72.9158
B	15	3760.38	250.692	129.5262
C	15	3781.2	252.08	103.6538
D	15	3625.08	241.672	136.1737
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	5663.1519	3	1887.7173	17.0730	0.0000	2.7694
Within Groups	6191.7728	56	110.5674
Total	11854.9247	59
			Level of significance			0.05

Tukey-Kramer Multiple Comparisons
	Sample	Sample			Absolute	Std. Error	Critical
Group	Mean	Size		Comparison	Difference	of Difference	Range	Results
1: A	227.6973	15		Group 1 to Group 2	22.99467	2.714987673	10.15	Means are different
2: B	250.692	15		Group 1 to Group 3	24.38267	2.714987673	10.15	Means are different
3: C	252.08	15		Group 1 to Group 4	13.97467	2.714987673	10.15	Means are different
4: D	241.672	15		Group 2 to Group 3	1.388	2.714987673	10.15	Means are not different
				Group 2 to Group 4	9.02	2.714987673	10.15	Means are not different
Other Data				Group 3 to Group 4	10.408	2.714987673	10.15	Means are different
Level of significance	0.05
Numerator d.f.	4
Denominator d.f.	56
MSW	110.5674
Q Statistic	3.74