Question

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.

1. Run the appropriate test in Minitab and show output. What conclusions can you make?
2. Obtain boxplots and residual plots for these data.
3. Are the assumptions of an ANOVA reasonably satisfied? Explain in reference to the plots.
4. 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.

Salary per course   Subject
1700 Humanities
1900   Humanities
1800 Humanities
2100 Humanities
2500   Humanities
2700   Humanities
2900   Humanities
2500   Humanities
2600   Humanities
2800   Humanities
2700   Humanities
2900   Humanities
2500   Social Sciences
2300   Social Sciences
2600   Social Sciences
2400   Social Sciences
2700   Social Sciences
2400   Social Sciences
2600   Social Sciences
2400   Social Sciences
2500   Social Sciences
3500   Social Sciences
3300   Social Sciences
3600   Social Sciences
3400   Social Sciences
2700   Engineering
2800   Engineering
2900   Engineering
3000   Engineering
2800   Engineering
2700   Engineering
3700   Engineering
3600   Engineering
3700   Engineering
3800   Engineering
3900   Engineering
2500   Managament
2600   Managament
2300   Managament
2800   Managament
3300   Managament
3400   Managament
3300   Managament
3500   Managament
3600   Managament

Answer 1

1. Run the appropriate test in Minitab and show output. What conclusions can you make?

Ans:

One-way ANOVA: Salary versus Subject

Source	DF	SS	MS	F	P
Subject	3	4167567	1389189	6.23	0.001
Error	41	9144878	223046
Total	44	13312444

S = 472.3 R-Sq = 31.31% R-Sq(adj) = 26.28%
Conclusion: The p-value for the test statistic F is 0.001. Hence, we can conclude that at least one mean salary of a subject has a significant difference from the remaining subjects at the 0.05 significance level.

2. Obtain boxplots and residual plots for these data.

Ans:

Boxplot of Salary 4000 3500 3000 2500 de 2000 Engineering Humanities Managament Social Sciences Subject

From the box-plot, the large part of the areas of the box-plot is overlap between the Engineering, Management, and Social Science subjects but the subject Humanities has at the lower. Hence, the mean salary of the Humanities subject may be different from the other remaining subjects.

Residual Plots for Salary Normal Probability Plot Versus Fits 1000 r 90 500 500 -1000 500 500 1000 2400 2600 280 3000 320 Residual Fitted Value Histogram Versus Order 1000 砂. 400 800 1 5 10 15 20 25 30 35 40 45 Observation Order Residual

From the histogram of the residuals, we know that residuals have a bimodal normal distribution. Hence, the assumption of a univariate normal distribution is violated.

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

Ans:

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

4. 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.

Ans:

Tukey 95% Simultaneous Confidence Intervals All Pairwise Comparisons among Levels of Subject Individual confidence level 98.94% Subject-Engineering subtracted from: Subject Humanities Managament Social Sciences -970.3-451.7 66.8 Lower Center Upper -1339.7-811.4 -283.0 -771.9-203.0 365.8 Subject-Humanities subtracted from: Subject Managament Social Sciences -147.1 359.6 866.3 Lower Center Upper 50.2 608.3 1166.4 Subject Managament subtracted from: Subject Social Sciences -797.6 -248.7 300.1 Lower Center Upper

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.