The university of Akron’s undergraduate advising office wants to know if student
ID: 3160562 • Letter: T
Question
The university of Akron’s undergraduate advising office wants to know if student preferences are changing in the CBA. Historically, students are divided over the different departments in the following proportions:
Major
Proportion
Accounting
0.33
Finance
0.20
Management
0.22
Marketing
0.25
For the Fall of 2016, the following numbers of students are registered: 65 accounting, 30 in Finance, 40 in Management, and 47 in marketing.
A. Does the pattern of student registrations for Fall of 2016 differ significantly from the historical pattern? Show your calculation (either by hand, or report the relevant information from your computer output) to support your conclusion:
Major
Proportion
Accounting
0.33
Finance
0.20
Management
0.22
Marketing
0.25
Explanation / Answer
As it is not given, we set alpha = 0.05.
Doing an observed/expected value table,
O E (O - E)^2/E
65 60.06 0.406320346
30 36.4 1.125274725
40 40.04 3.996E-05
47 45.5 0.049450549
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 1.581085581
As df = a - 1,
a = 4
df = a - 1 = 3
Then, the critical chi^2 value is
significance level = 0.05
chi^2(crit) = 7.814727903
Also, the p value is
p = 0.663686101
As chi^2 < 7.815, and Pvalue > 0.05, we FAIL TO REJECT THE NULL HYPOTHESIS.
Thus, there is no significant evidence that the pattern of student registrations for Fall of 2016 differ significantly from the historical pattern. [CONCLUSION]
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