The faculty council of a large university would like to determine the opinion of
ID: 3322297 • Letter: T
Question
The faculty council of a large university would like to determine the opinion of various groups toward a proposed trimester academic calendar. A random sample of 100 undergraduate students, 50 graduate students, and 50 faculty members is selected with the following results. At the .01 level of significance, is there evidence of a difference in attitude toward the trimester between the various groups?
Opinion
Undergraduate
Graduate
Faculty
Favor trimester
63
27
30
Oppose trimester
37
23
20
Opinion
Undergraduate
Graduate
Faculty
Favor trimester
63
27
30
Oppose trimester
37
23
20
Explanation / Answer
The Expected value data are in the table below. Each Cell = Row total * Column Total/N. N = 200
The degrees of freedom = (r – 1) * (c -1) = (2 - 1) * (3 - 1) = 2
The Hypothesis:
H0: There is no difference in attititude towards the trimester between the various groups.
Ha: There is a difference in attititude towards the trimester between the various groups.
The Test Statistic: The table below gives the calculation of 2.
2test = 1.125
The Critical Value: The critical value at = 0.05 , df = 1
2critical = 5.9915
The Decision Rule: If 2 test is > 2 critical, then Reject H0.
The Decision: Since If 2 test (1.125) is < 2 critical (5.9915), We Fail to reject H0.
The Conclusion: There is insufficient evidence at the 95% significance level to conclude that there is a difference in attititude towards the trimester between the various groups.
Observed Undergraduate Graduate Faculty Total Favor Trimester 63 27 30 120 Oppose Trimester 37 23 20 80 Total 100 50 50 200 Expected Undergraduate Graduate Faculty Total Favor Trimester 60.00 30.00 30.00 120 Oppose Trimester 40.00 20.00 20.00 80 Total 100 50 50 200Related Questions
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