Question

In: Statistics and Probability

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 2 years ago
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