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

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 e of Variati Between groups Within groups (error) Total 19 36 133 (a) Complete the F-table. (Round your values for mean squares and F to two decimal places.) of Variati df Betwe en groups 19 36 133 Within groups (error) Total (b) Compute omega-squared (ae). (Round your answer to two decimal places.) (c) Is the decision to retain or reject the null hypothesis? (Assume alpha equal to 0.05.) O Retain the null hypothesis. O Reject the null hypothesis. You may need to use the appropriate table in Appendix C to answer this question.

Explanation / Answer

a) Degree of freedom between group (DFB) = number of groups - 1

Here, number of groups = 4 (unemployed, retired, part-time employees, full-time employees)

DFB = 4-1 = 3

Sum of squares of between groups (SSB) = Mean square of between groups (MSB) * DFB

Here, MSB = 19 (from the table)

SSB = 19 * 3 = 57

Sum of squares of within group (SSW) = Sum of squares Total (SST) - SSB

Here, SST = 133 (from the table)

SSB = 57 (calculated in the above steps)

SSW = 133 - 57 = 76

Mean square within group (or Mean square Error) (MSW) = SSW / degree of freedom within group (DFW)

Here, DFW = 36 (from the given table)

SSW = 76 (calculated above)

MSW = 76 / 36 = 2.11

F value = Mean square of between groups (MSB) / Mean square of within groups (MSW)

Here, MSB = 19 (from the given table)

MSW = 2.11 (calculated above)

F value = 19 / 2.11 = 9.01

b) Omega2 between group = (SSB - (DFB * MSW)) / (MSW + SST)

(all the values are obtained in the above calculations)

Omega2 between group = (57 - (3*2.11)) / (2.11 +133) = 0.38

c) Alpha = 0.05

F value = 9.01

p value for df1=3 and df2=36 is 2.87

as p value is large H0 should be accepted

  

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