Question

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			24
Within groups (error)		36
Total	152

(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			24
Within groups (error)		36
Total	152

(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.    

You may need to use the appropriate table in Appendix C to answer this question.

webassign.net/priviterastats3/priviterastats3_appendix_c.pdf

Answer 1

Given:

a)

The following is an incomplete F-table summarizing the results of a study of the variance of life satisfaction scores among 1) unemployed, 2) retired, 3) part-time, and 4) full-time employees.

Thus k = Number of groups = 4

Source of Variation	SS	df	MS	F
Between groups			24
Within groups (error)		36
Total	152

We have to complete the F-table.

df_between = k - 1

df_between = 4 - 1

df_between = 3

MS_between = 24

thus

MS_between = SS_between / df_between

24 = SS_between / 3

SS_between = 24 X 3

SS_between = 72

We have:

SS_total = 152

thus

SS_within = SS_total - SS_between

SS_within = 152 - 72

SS_within = 80

and

df_within  = 36

thus

MS_within =SS_within / df_within  

MS_within = 80 / 36

MS_within = 2.22

and

df_total = df_between +  df_within  

df_total = 3 + 36

df_total = 39

Thus

F = MS_between / MS_within  

F = 24 / 2.22

F = 10.8

thus

Source of Variation	SS	df	MS	F
Between Groups	72	3	24	10.8
Within Groups	80	36	2.22
Total	152	39

b)

Compute omega-squared (ω²).

= 72 - (3 *2.22) / (152+2.22)

= (72 - 6.66) / 154.22

= 0.42

c) p value 0.000 < 0.05 ()

so, reject the null hypothesis.