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A dean wants to check the consistency of teaching quality among the faculty in one of the departments. A sample of students was obtained from three classes taught by three different faculty, and their common final exam scores were recorded.

Classes

Final Exam Scores

Class 1

70	71	73	77	53	72	67	73

Class 2

74	58	59	54	73	81	71	62	76	82

Class 3

68	73	64	84	81	78	65	53

Class 4

77	87	62	84	77	69	82	78	62

Class 5

52	70	84	68	63	78	62	60	72	73

Can you conclude that the teaching quality is inconsistent among the courses? Use the level of significance 10%.

Procedure:

Assumptions: (select everything that applies)

All expected frequencies are 1 or greater
At most 20% of the expected frequencies are less than 5
Equal population standard deviations
Simple random sample
Normal populations
Independent samples

Step 1. Hypotheses Set-Up:

\displaystyle {H}_{{0}}:

\displaystyle {H}_{{a}}:

, and the test is

Step 2. The significance level $\displaystyle \alpha=$ %

Step 3. With the total number of observations, n=, and the number of populations, k=, compute the value of the test statistic using the table below:

Source	DF	SS	MS	F	P
Duration	k-1=	294.1416	73.5354	0.851	0.502
Error	n-k=	3455.1	86.3775
Total	44	3749.2416

The test statistic is = (Round the answer to 3 decimal places)

with the degrees of freedom (dfn=,dfd=)

Step 4. Testing Procedure: (Round the answers to 3 decimal places)

CVA	PVA
Provide the critical value(s) for the Rejection Region:	Compute the P-value of the test statistic:
left CV is and right CV is	P-value is

Step 5. Decision:

CVA	PVA
Is the test statistic in the rejection region?	Is the P-value less than the significance level?

Conclusion:

Step 6. Interpretation:

At 10% significance level we have sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.

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