You are the director of the Bison University Marching band. You decide to grade

Question

You are the director of the Bison University Marching band. You decide to grade themembers of the band based upon the number of times each member provides anoutstanding performance. To test your grading method, you try it for a sample of 4subjects from four sections of the band: the clarinets, the flutes, the trumpets, and thedrums. The table below summarizes your scores:   

Outstanding Band Performances by Sections  

Test, using ANOVA, to see if the mean number of outstanding performances by each of the bandsections is equal at the .05 level.

Clarinets Flutes Trumpets Drums 1 5 1 4 2 6 7 5 1 3 3 6 4 5 8 4

Explanation / Answer

Here one way ANOVA will be used. Following is the output of one way ANOVA analysis:

The F test statistics is

F = 1.96

The p-value is

p-value = 0.1736

Since p-value is greater than 0.05 so we can conclude that the mean number of outstanding performances by each of the bandsections is equal at the .05 level.

One factor ANOVA Mean n Std. Dev 2.0 4 1.41 Clarinets 4.8 4 1.26 Flutes 4.8 4 3.30 Trumpets 4.8 4 0.96 Drums 4.1 16 2.14 Total ANOVA table Source SS    df MS F    p-value Treatment 22.69 3 7.563 1.96 .1736 Error 46.25 12 3.854 Total 68.94 15

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