Problem 1.20 points Engineers specialized in tennis equipment performed an exper
ID: 3363373 • Letter: P
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Problem 1.20 points Engineers specialized in tennis equipment performed an experiment to determine the effect of the racket brand and the ball brand on the speed of a tennis ball (in miles per hour). Five racket brands were randomly selected and two ball brands were randomly selected. An individual hit a forehand three times for each combination of racket brand and ball brand. The data are shown in the table below Ball Brand 1 Ball Brand 2 Racket Brand 1 2 31 2 3 50 4950 5048 51 5252 515151 51 5350 5054 5251 49 51 5048 50 51 48 49 4848 49 48 4 (a) [10 points] Analyze the data from this experiment. (b) [5 points Estimate the variance components (c) [5 points] Repeat part (a) assuming that the engineers are interested in those specific five racket brands (the two ball brands are still randomly selected)Explanation / Answer
a)
Two-way ANOVA: speed versus Racket, Ball
Source DF SS MS F P
Racket 4 44.0000 11.0000 9.07 0.000
Ball 2 0.2667 0.1333 0.11 0.896
Error 23 27.9000 1.2130
Total 29 72.1667
S = 1.101 R-Sq = 61.34% R-Sq(adj) = 51.25%
Comment: The estimated p-value of Racket is 0.000. Hence, we can conclude that atleast one racket has significant speed than remaining racket at 0.05 level of significance.
The estimated p-value of the ball is 0.896. Hence, we can conclude that speed of ball does not significant by using different ball types at 0.05 level of significance.
b) The estimated variance is 1.2130.
c)
One-way ANOVA: speed versus Racket
Source DF SS MS F P
Racket 4 44.00 11.00 9.76 0.000
Error 25 28.17 1.13
Total 29 72.17
S = 1.061 R-Sq = 60.97% R-Sq(adj) = 54.73%
Comment: The estimated p-value of Racket is 0.000. Hence, we can conclude that at least one racket has significant speed than remaining racket at 0.05 level of significance.
Compare the R-Sq(adj) values between the two model, the last model is best because decrease the parameter increase the R-Sq(adj) value.
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