Three “recipes” for manufacturing billiard balls are to be compared. The elastic

Question

Three “recipes” for manufacturing billiard balls are to be compared. The elasticity of ten billiard balls made by each recipe is measured. Ignore the column headed “Batch”. Do the three recipes produce the same mean elasticity? Use the Analysis of Variance (ANOVA) and includes the null and alternative hypotheses, an ANOVA table and a clear conclusion, which should include a p-value.

Elasticity of Billiard Balls Batch Control Additive A 75 51 73 49 66 66 73 58 71 78 10 Additive B 39 43 43 42 41 44

Explanation / Answer

The null and alternative hypotheses will be:

Ho: The mean elasticity produced by all three reciepes are same.

Ha: Mean elasticity produced by atleast one reciepe is different.

The ANOVA table will be:

ANOVA table

Since p - value is almost close to 0, we reject Ho.

Hence,

We have sufficient evidence to conclude that the mean elasticity produced by atleast one reciepe is different.

Source DF SS MS F-Stat P-value Reciepe 2 5654.867 2827.433 51.86 <0.0001 Error 27 1472.1 54.522 Total 29 7126.967

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