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	6
5	5	7
5	4	5
3	3	7
2	7	4
3	4	7
5	5	5
3	2	7

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

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.

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 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

H: Hure = HT a auditor = Hrast-food worker H: At least two of the population means are different. EXCEL (Data Analysis) output: Anova: Single Factor Sum SUMMARY Groups Nurse Tax auditor Fast-Food worker Count 8 8 8 30 34 48 Average Variance 3.75 1.357143 4.25 2.214286 6 1.428571 F ANOVA Source of Variation Between Groups Within Groups Total SS 22.33333 35 57.33333 df MS 2 11.16667 21 1.666667 P-value 6.7 0.005616 Fcrit 3.4668 The value of the test statistic is F =6.70.

p-value = 0.006. Reject H. There is sufficient evidence to conclude that there is a difference in mean scores for the three professions. (6) LSD =to 03 đợt MSW (1 +1/ng) = 2.030, 1.6667 (278) = 2.030(0.6455) =131 Iwwe - Foreldtoy = 13.75 -4.25|=0.5. There is not a significant difference between the means for nurses and tax auditors.