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 3 4 5 4 5 8 6 4 6 2 4 8 3 6 5 3 3 6 4 5 6 5 3 4 (a) Use ? = 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: μNurse = μTax auditor = μFast-food worker Ha: μNurse ≠ μTax auditor ≠ μFast-food worker H0: At least two of the population means are equal. Ha: At least two of the population means are different. H0: Not all the population means are equal. Ha: μNurse = μTax auditor = μFast-food worker H0: μNurse = μTax auditor = μFast-food worker Ha: Not all the population means are equal. H0: μNurse ≠ μTax auditor ≠ μFast-food worker Ha: μNurse = μTax auditor = μFast-food worker 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. (A) Do not reject H0. There is not sufficient evidence to conclude that there is a difference in mean scores for the three professions. (B) Reject H0. There is not sufficient evidence to conclude that there is a difference in mean scores for the three professions. (C) Reject H0. There is sufficient evidence to conclude that there is a difference in mean scores for the three professions. (D) Do not reject H0. There is 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 ? = 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. |xNurse − xTax auditor | = _______ What conclusion can you draw after carrying out this test? (A) There is a significant difference between the means for nurses and tax auditors. (B) There is not a significant difference between the means for nurses and tax auditors.
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 |
|---|---|---|
| 3 | 4 | 5 |
| 4 | 5 | 8 |
| 6 | 4 | 6 |
| 2 | 4 | 8 |
| 3 | 6 | 5 |
| 3 | 3 | 6 |
| 4 | 5 | 6 |
| 5 | 3 | 4 |
(a) Use ? = 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: μNurse = μTax auditor = μFast-food worker
Ha: μNurse ≠ μTax auditor ≠ μFast-food worker
H0: At least two of the population means are equal.
Ha: At least two of the population means are different.
H0: Not all the population means are equal.
Ha: μNurse = μTax auditor = μFast-food worker
H0: μNurse = μTax auditor = μFast-food worker
Ha: Not all the population means are equal.
H0: μNurse ≠ μTax auditor ≠ μFast-food worker
Ha: μNurse = μTax auditor = μFast-food worker
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.
(A) Do not reject H0. There is not sufficient evidence to conclude that there is a difference in mean scores for the three professions.
(B) Reject H0. There is not sufficient evidence to conclude that there is a difference in mean scores for the three professions.
(C) Reject H0. There is sufficient evidence to conclude that there is a difference in mean scores for the three professions.
(D) Do not reject H0. There is 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 ? = 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.
|xNurse − xTax auditor | = _______
What conclusion can you draw after carrying out this test?
(A) There is a significant difference between the means for nurses and tax auditors.
(B) There is not a significant difference between the means for nurses and tax auditors.
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