1 One characteristic of billiard balls is their elasticityth

1. One characteristic of billiard balls is their elasticity—the bounce they get when striking one another. A manufacturer of billiard balls is testing three additives to the basic plastic. A partial ANOVA table is

Source DF SS

additive 2 5654.9

error 27 1472.1

total 29 7127.0

The F statistic for the ANOVA is F = 51.86. The P-value for the test is p > 0.01. p < 0.001. 0.001 < p < 0.01.

Solution

1. the sum of squares of additive is given as SS=5654.2 with df=2

hence the mean of squares of additive=MSA=SS/df=5654.2/2=2827.1

the sumf of squares of error is given as 1472.1 with df=27

hence the mean of squares of error=MSE=1472.1/27=54.52

so to test the performance of three additives to the basic plastic the test statistic is

F=MSA/MSE which under H0 follows an F distribution with dfs= df of additive and df of error i.e, the dfs are 2,27

now the value of F is 2827.1/54.52=51.86

in ANOVA a right tailed test is always used.

so the p value is P[F>51.86] where F follows an F distribution with dfs 2 and 27

so using minitab p value=P[F>51.86]=0.0000

hence the correct alternative is p<0.001 [answer]