Question

# Consider the partial ANOVA table shown below. Let a = .01 Source of Variation DF SS...

Consider the partial ANOVA table shown below. Let a = .01

 Source of Variation DF SS MS F Between Treatments 3 180 Within Treatments (Error) Total 19 380

If all the samples have five observations each:

 there are 10 possible pairs of sample means. the only appropriate comparison test is the Tukey-Kramer. all of the absolute differences will likely exceed their corresponding critical values. there is no need for a comparison test – the null hypothesis is not rejected.

2 points

QUESTION 2

Consider the partial ANOVA table shown below. Let a = .01

 Source of Variation DF SS MS F Between Treatments 3 180 Within Treatments (Error) Total 19 380

The mean square within treatments (MSE) is

 12.5 200 16 60

2 points

QUESTION 3

Consider the partial ANOVA table shown below:

 Source of Variation DF SS MS F Between Treatments 64 8 Within Treatments (Error) 2 Total 100

The number of degrees of freedom corresponding to within treatments is

 20 18 4 5

2 points

QUESTION 4

Consider the following ANOVA table.

 Source of Variation SS df MS F Treatment 49411.11 2 24705.56 10.4304 Error 35529.17 15 2368.611 Total 84940.28 17

The appropriate null hypothesis is:

 mu1 = mu2 mu1 = mu2 = mu3 At least one mean is different. The populations are independent.

2 points

QUESTION 5

The following information is from a 1-way ANOVA involving three treatments:

 Treatment 1 Treatment 2 Treatment 3 Sample Size 5 10 5 Sample Mean 4 8 9

The overall mean for all the treatments is

 7.25 4.89 6.67 7

 source df SS MS F Fcrit between 3 180 60 4.8 5.29 within 16 200 12.5 total 19 380

1)

there is no need for a comparison test – the null hypothesis is not rejected.

2)

mean square within treatments (MSE) is =12.5

3)

 source df SS MS F Fcrit between 4 64 16 8 4.58 within 18 36 2 total 22 100

number of degrees of freedom corresponding to within treatments is =18

4)

mu1 = mu2 = mu3

5)

overall mean for all the treatments is =(4*5+8*10+9*5)/(5+10+5)=7.25

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