Question

The following is an incomplete F-table summarizing the results of a study of the variance of...

The following is an incomplete F-table summarizing the results of a study of the variance of life satisfaction scores among unemployed, retired, part-time, and full-time employees.

Source of Variation SS df MS F
Between groups       18   
Within groups (error)    36      
Total 130         

(a) Complete the F-table. (Round your values for mean squares and F to two decimal places.)

Source of Variation SS df MS F
Between groups 18
Within groups (error) 36   
Total 130      


(b) Compute omega-squared

(ω2).

(Round your answer to two decimal places.)
ω2 =  

(c) Is the decision to retain or reject the null hypothesis? (Assume alpha equal to 0.05.)

Retain the null hypothesis.Reject the null hypothesis.     


Homework Answers

Answer #1

a)

There are 4 groups:unemployed, retired, part-time, and full-time employees. So, k=4

Here' how the ANOVA F table can be calculated by hand:

and

SS df MS F
Between SS(B) k-1 SS(B)/(k-1) MS(B)/MS(W)
Within SS(W) N-k SS(W)/(N-k)
Total SS(W)+SS(B) N-1

Using the basic mathematics i have filled table: So the table looks like:

dfb = 4-1 =3. SSb =df*MS = 3*18 =54

SSt = 130, so SSe = 130-54=76, MSe = SSe/dfe = 2.1111

F = MSb/MSe   = 18/2.111 = 8.526

SS df MS F
Between groups 54 3 18 8.526316
Within groups (error) 76 36 2.111111
Total 130 39

b)

Where SSb = 54, k=4, MSe = 2.111, SSt = 130.

We get ω2 = 0.36

c)

We reject the null hypothesis as probability against F(3,36,8.526) is 0.9998.

because this lies well within the rejection region of alpha=.05( 1-0.05 = 0.95).

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