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In: Statistics and Probability

A researcher investigates the factors that are associated with the salaries of professors who teach courses...

A researcher investigates the factors that are associated with the salaries of professors who teach courses at a major university. The researcher gathers data about the subject area and the salary per course for a random sample of professors. Data are found in the file Academic Salaries by Subject Area.

Salary per course Subject Salary per course Subject Salary per course Subject Salary per course Subject
1700 Humanities 2500 Social Sciences 2700 Engineering 2500 Managament
1900 Humanities 2300 Social Sciences 2800 Engineering 2600 Managament
1800 Humanities 2600 Social Sciences 2900 Engineering 2300 Managament
2100 Humanities 2400 Social Sciences 3000 Engineering 2800 Managament
2500 Humanities 2700 Social Sciences 2800 Engineering 3300 Managament
2700 Humanities 2400 Social Sciences 2700 Engineering 3400 Managament
2900 Humanities 2600 Social Sciences 3700 Engineering 3300 Managament
2500 Humanities 2400 Social Sciences 3600 Engineering 3500 Managament
2600 Humanities 2500 Social Sciences 3700 Engineering 3600 Managament
2800 Humanities 3500 Social Sciences 3800 Engineering
2700 Humanities 3300 Social Sciences 3900 Engineering
2900 Humanities 3600 Social Sciences
3400 Social Sciences
  1. State the null and alternate hypothesis we would run to determine if the average salaries of the professors is the same across all sujcet areas.
  2. Run the appropriate test in Minitab and show output. What conclusions can you make?
  3. Obtain boxplots and residual plots for these data.
  4. Are the assumptions of an ANOVA reasonably satisfied? Explain in reference to the plots.
  5. If there is a difference in salaries run a Tukey’s test to show how the salaries for the different subject areas compare to each other. Describe what the results of the Tukey’s test tell you.

Solutions

Expert Solution

Answer:

d)Are the assumptions of an ANOVA reasonably satisfied? Explain in reference to the plots.

The assumptions of an ANOVA reasonably do not satisfy because of the bimodal from residuals histogram. Out assumption unimodal normal distribution on residuals.

From the above Tuke's test, the confidence intervals of Humanities VS Engineering and Humanities VS Management does not include the value zero. Hence, we can conclude that the salary per course between the Humanities & Engineering and Humanities & Management have a significant difference at the 0.05 significance level.

orchestra answered 2 years ago
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