Question

Chapter 12 WebAssign

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			16
Within groups (error)		36
Total	124

(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			16
Within groups (error)		36
Total	124

(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.    

Answer 1

As per the given information:

MSB (mean square between) = 16

df_B (degrees of freedom error) = 36

TSS (total sum square) = 124

Total number of treatments (k) = 4 (unemployed, retired, part-time, and full-time employees)

(a). The calculation of rest of the missing values is shown below:

The complete ANOVA table:

Source of variation	SS	df	MS	F
Between groups	48	3	16	7.58
Within groups (error)	76	36	2.11
Total	124	40

(b). The omega squared, can be calculated as,

Therefore, the omega squared is 0.33

(c). At the significance level 0.05 and the degrees of freedom (3, 36), the critical value obtained from the f-table is 2.866.

Since, the test statistic (7.58) is greater than the critical value (2.866), so the researcher will reject the null hypothesis.