roblem 2: Chi-Square Independence Test (20 points, 4 points/each question) The d
ID: 3318153 • Letter: R
Question
roblem 2: Chi-Square Independence Test (20 points, 4 points/each question) The director of a dmissions at a state college is interested in seeing if admissions status (admitted, waiting list, denied admission) at his college is independent of the type of community in which an applicant resides. He takes a sample of recent admissions decisions and forms the following table Admitted Wait List DeniedTotal Urban Rural Suburban 21 13 12 46 83 70 85 238 45 34 112 24 39 80 He will use this table to do a chi-square test of independence with a 1% significance level. 1. Specify the hypothesis for this independence testExplanation / Answer
The Expected value data are in the table below. Each Cell = Row total * Column Total/N. N = 238
The Hypothesis:
H0: There is no relation between admission status and type of community in which the application resides. (They are independent of each other).
Ha: There is a relation between admission status and type of community in which the application resides. (They are not independent of each other).
The Test Statistic: The table below gives the calculation of 2.
2test = 12.62
The Critical Value: The critical value at = 0.01, degrees of freedom = (r – 1) * (c -1) = (3 -1) * (3 -1) = 4
2critical = 13.28
The Decision Rule: If 2 test is > 2 critical, then Reject H0.
The Decision: Since If 2 test (12.62) is < 2 critical (13.28), We Fail to reject H0.
The Conclusion: There is insufficient evidence at the 99% significance level to conclude that there is a relation between admission status and type of community in which the application resides.
(or there is insufficient evidence to conclude that they are independent of each other).
Observed Admitted Wait List Denied Total Urban 45 21 17 83 Rural 33 13 24 70 Suburban 34 12 39 85 Total 112 46 80 238 Expected Admitted Wait List Denied Total Urban 39.06 16.04 27.90 83 Rural 32.94 13.53 23.53 70 Suburban 40.00 16.43 28.57 85 Total 112 46 80 238Related Questions
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