Question

The following table gives the distributions of grades for three professors for a few randomly selected classes that each of them taught during the last 2 years. Professor Grades McQueen Walker Sam A 18 36 20 B 25 44 15 C, 85 73 82 D&F 17 12 Using a 2.5% significance level, test the null hypothesis that the grade distributions are homogeneous for these three professors. (37.5 points) Hints: Identify your hypotheses in words, state your hypotheses, calculate the test statistics, and summarize your finding in context to the story problem).

Answer 1

	Mean	n	Std. Dev
	36.250	4	32.694	Treatment 1
	41.250	4	25.158	Treatment 2
	31.250	4	34.189	Treatment 3
	24.667	3	9.866	Block 1
	28.000	3	14.731	Block 2
	80.000	3	6.245	Block 3
	12.333	3	4.509	Block 4
	36.250	12	28.304	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatments	200.00	2	100.000	1.10	.3928
Blocks	8,064.92	3	2,688.306	29.47	.0005
Error	547.33	6	91.222
Total	8,812.25	11

The hypothesis being tested is:

H0: The grade distributions are homogeneous for the three professors

Ha: The grade distributions are not homogeneous for at least one professor

The p-value is 0.3928.

Since the p-value (0.3928) is greater than the significance level (0.025), we fail to reject the null hypothesis.

Therefore, we can conclude that the grade distributions are homogeneous for the three professors.

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