Questions 30-31: Given the following Analysis of Variance table for three treatm

Question

Questions 30-31: Given the following Analysis of Variance table for three treatments each with six-observations.

Source:                    Sum of Squares:                        df:                      Mean Square:

Treatments                                                                    2

Error                                                                                                                20

Total                           780

30.) What is the size of total variation for treatments?

A.) 780

B.) 300

C.) 480

D.) 200

E.) 450

What are the test statistic value of F and the critical value of F at the 1% level of significance? Show your solution.

A.) 11 and 6.36

B.) 12 and 6.36

C.) 11 and 3.68

D.) 12 and 3.68

E.) 12 and 6.23

Explanation / Answer

We have 3 groups and 6 participants per group so we have a total of 3*6=18 individuals so total degrees of freedom is 18-1 =17

This also means that Error degrees of freedom is thus 17-2=15 (because treatment df is 2)

For Error term, SS=df*Mean square =15*20=300

Thus for treatement term it is 780-300=480 (total-error)

So correct answer for part 1 is C

Mean square for error term is 480/2=240

Also F statistic is (Treatment Mean sqaure)/(Error mean sqaure) =240/20=12

Using F table for 1% level of significance

Df in numerator is 2 and denominator is 15, refer F statistic table to get value of answer as 6.23 thus option E is right

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