A sporting goods manufacturing company wanted to compare the distance traveled by golf balls produced using...

A sporting goods manufacturing company wanted to compare the distance traveled by golf balls produced using each of 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 provided in the Excel file Golfball.

a). At the .05 level of significance, is there evidence of a difference in the mean distances traveled by the golf balls with different designs?

b). What assumptions are necessary in (a)?

Design1	Design2	Design3	Design4
206.67	217.43	227.12	230.90
208.29	221.78	225.14	228.30
206.54	218.39	230.10	232.19
204.80	224.48	228.86	225.22
210.00	212.17	221.79	229.84
204.16	214.25	224.20	231.45
207.10	221.63	224.32	221.88
206.03	229.78	234.65	235.80
204.84	213.89	219.85	228.70
211.21	214.86	233.35	225.44

I need help how to solve in Excel !!!

Solutions

Expert Solution

from excel > menu>data > data analysis> choose anova single factor

o/p obtained is

Anova: Single Factor

SUMMARY
Groups	Count	Sum	Average	Variance
Design1	10	2069.64	206.964	5.246427
Design2	10	2188.66	218.866	30.66718
Design3	10	2269.38	226.938	23.18213
Design4	10	2289.72	228.972	16.10697


ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	2990.99	3	996.9966	53.02982	2.73E-13	2.866266
Within Groups	676.8244	36	18.80068

Total	3667.814	39

test stat = 53.03

p value = 0.000

Decision:   p-value<α , reject null hypothesis

conclusion :    there is enough evidence of significance difference among three treatments

there is evidence of a difference in the mean distances traveled by the golf balls with different designs

b) three assumptions for ANOVA analysis, namely, independence, equal variance, and normality.

orchestra answered 1 year ago

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