Question

A research study concluded that self-employed individuals do not experience higher job satisfaction than individuals who are not self-employed. In this study, job satisfaction is measured using 18 items, each of which is rated using a Likert-type scale with 1–5 response options ranging from strong agreement to strong disagreement. A higher score on this scale indicates a higher degree of job satisfaction. The sum of the ratings for the 18 items, ranging from 18–90, is used as the measure of job satisfaction. Suppose that this approach was used to measure the job satisfaction for lawyers, physical therapists, cabinetmakers, and systems analysts. Suppose the results obtained for a sample of 10 individuals from each profession follow.

Lawyer	Physical Therapist	Cabinetmaker	Systems Analyst
42	53	52	44
40	78	65	71
76	82	77	73
42	88	69	58
51	62	77	64
48	59	62	68
43	64	61	41
46	52	78	55
66	57	86	78
40	48	60	64

At the α = 0.05 level of significance, test for any difference in the job satisfaction among the four professions.

State the null and alternative hypotheses.

H₀: Not all the population means are equal.
H_a: μ_L = μ_PT = μ_C = μ_SAH₀: μ_L ≠ μ_PT ≠ μ_C ≠ μ_SA
H_a: μ_L = μ_PT = μ_C = μ_SA    H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.H₀: μ_L = μ_PT = μ_C = μ_SA
H_a: μ_L ≠ μ_PT ≠ μ_C ≠ μ_SAH₀: μ_L = μ_PT = μ_C = μ_SA
H_a: Not all the population means are equal.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Do not reject H₀. There is sufficient evidence to conclude that the mean job satisfaction rating is not the same for the four professions.Do not reject H₀. There is not sufficient evidence to conclude that the mean job satisfaction rating is not the same for the four professions.    Reject H₀. There is not sufficient evidence to conclude that the mean job satisfaction rating is not the same for the four professions.Reject H₀. There is sufficient evidence to conclude that the mean job satisfaction rating is not the same for the four professions.

Answer 1

The statistic software output for this problem is:

Analysis of Variance results: Data stored in separate columns. Column statistics n Mean Std. Dev. Std. Error Column Lawyer 10 49.4 12.139925 3.8389813 64.3 13.7198154.3385866 Physical Therapist 10 Cabinetmaker 10 68.7 10.520351 3.326827 Systems Analyst 10 61.6 12.158216 3.8447656 ANOVA table P-value Source DF SS MS F-Stat Columns 3 2051 683.66667 4.6029549 0.0079 Error 36 5347 148.52778 Total 39 7398

Test statistics = 4.60

P-value = 0.008

Reject H₀. There is sufficient evidence to conclude that the mean job satisfaction rating is not the same for the four professions.