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. Data are found in the file Academic Salaries by Subject Area.

a) State the null and alternate hypothesis we would run to determine if the average salaries of the professors is the same across all subjcet areas.

b) Run the appropriate test in Excel and show output. What conclusions can you make?

c) Obtain boxplots for these data, each individual data NPP, and a NPP for all residuals.

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

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

Answer 1

a) State the null and alternate hypothesis we would run to determine if the average salaries of the professors is the same across all subjcet areas.

The hypothesis being tested is:

H₀: µ₁ = µ₂ = µ₃ = µ₄

H_a: At least one means is not equal

b) Run the appropriate test in Excel and show output. What conclusions can you make?

The output is:

	Mean	n	Std. Dev
	2,425.0	12	435.11	Humanities
	2,784.6	13	477.57	Social Sciences
	3,236.4	11	494.52	Engineering
	3,033.3	9	484.77	Managament
	2,848.9	45	550.05	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	41,67,566.82	3	13,89,188.941	6.23	.0014
Error	91,44,877.62	41	2,23,045.796
Total	1,33,12,444.44	44

Since the p-value (0.0014) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we cannot conclude that the average salaries of the professors are the same across all subject areas.

c) Obtain boxplots for these data, each individual data NPP, and a NPP for all residuals. (2 Marks)

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

The assumptions are:

The population from which samples are drawn should be normally distributed.
Independence of cases: the sample cases should be independent of each other.
Homogeneity of variance: Homogeneity means that the variance among the groups should be approximately equal.

These assumptions are met.

e) 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. (2 Marks)

Tukey simultaneous comparison t-values (d.f. = 41)
		Humanities	Social Sciences	Managament	Engineering
		2,425.0	2,784.6	3,033.3	3,236.4
Humanities	2,425.0
Social Sciences	2,784.6	1.90
Management	3,033.3	2.92	1.21
Engineering	3,236.4	4.12	2.33	0.96
critical values for experimentwise error rate:
		0.05	2.68
		0.01	3.32

The difference between Management and Humanities is significant.

The difference between Engineering and Humanities is significant.

All other differences are insignificant.