Question

A Pew Research study conducted in 2017 found that approximately 75% of Americans believe that robots and computers might one day do many of the jobs currently done by people.† Suppose we have the following data collected from nurses, tax auditors, and fast-food workers in which a higher score means the person feels his or her job is more likely to be automated.

Nurse	Tax Auditor	Fast-Food Worker
4	4	5
4	5	7
5	5	6
2	3	7
2	7	4
3	3	6
5	5	5
5	2	8

(a)

Use α = 0.05 to test for differences in the belief that a person's job is likely to be automated for the three professions.

State the null and alternative hypotheses.

H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.

H₀: Not all the population means are equal.
H_a: μ_Nurse = μ_{Tax auditor} = μ_{Fast-food worker}  

H₀: μ_Nurse ≠ μ_{Tax auditor} ≠ μ_{Fast-food worker}
H_a: μ_Nurse = μ_{Tax auditor} = μ_{Fast-food worker}

H₀: μ_Nurse = μ_{Tax auditor} = μ_{Fast-food worker}
H_a: μ_Nurse ≠ μ_{Tax auditor} ≠ μ_{Fast-food worker}

H₀: μ_Nurse = μ_{Tax auditor} = μ_{Fast-food worker}
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 there is a difference in mean scores for the three professions.

Reject H₀. There is sufficient evidence to conclude that there is a difference in mean scores for the three professions.   

Do not reject H₀. There is not sufficient evidence to conclude that there is a difference in mean scores for the three professions.

Reject H₀. There is not sufficient evidence to conclude that there is a difference in mean scores for the three professions.

(b)

Use Fisher's LSD procedure to compare the belief that a person's job will be automated for nurses and tax auditors. (Use α = 0.05.)

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

LSD =

Find the pairwise absolute difference between sample means for nurses and tax auditors

= x_Nurse − x_{Tax auditor}

What conclusion can you draw after carrying out this test?

There is a significant difference between the means for nurses and tax auditors.

There is not a significant difference between the means for nurses and tax auditors.    

Answer 1

Applying one way ANOVA: (use excel: data: data analysis: one way ANOVA: select Array):

Source	SS	df	MS	F	P value
Between	22.33	2	11.17	5.72	0.0104
Within	41.00	21	1.95
Total	63.33	23

a)

H₀: μ_Nurse = μ_{Tax auditor} = μ_{Fast-food worker}
H_a: Not all the population means are equal

value of the test statistic=5.72

p-value =0.010

Reject H₀. There is sufficient evidence to conclude that there is a difference in mean scores for the three professions

b)

critical value of t with 0.05 level and N-k=21 degree of freedom=				tN-k=	2.080
Fisher's (LSD) for group i and j =(tN-k)*(sp*√(1/ni+1/nj)   =					1.45

x_Nurse − x_{Tax auditor} =0.5

There is not a significant difference between the means for nurses and tax auditors.