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	55	56	42
44	78	67	75
72	78	81	73
44	84	67	58
55	58	77	66
52	59	66	64
45	64	57	43
50	52	80	55
64	55	82	76
38	52	58	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: μ_L ≠ μ_PT ≠ μ_C ≠ μ_SA
H_a: μ_L = μ_PT = μ_C = μ_SAH₀: Not all the population means are equal.
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: Not all the population means are equal.H₀: μ_L = μ_PT = μ_C = μ_SA
H_a: μ_L ≠ μ_PT ≠ μ_C ≠ μ_SA

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 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.

Answer 1

The statistical software output for this problem is :

H₀: μ_L = μ_PT = μ_C = μ_SA
H_a: Not all the population means are equal.

Test statistics = 4.41

P-value = 0.007

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