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In: Statistics and Probability

Do male and female college students have the same distribution of living arrangements? Use a level...

Do male and female college students have the same distribution of living arrangements? Use a level of significance of 0.05. Suppose that 121 randomly selected male college students and 82 randomly selected female college students were asked about their living arrangements: dormitory, apartment, or other. The results are shown in Table. Do male and female college students have the same distribution of living arrangements?

Dormitory Apartment Other
Male 52 34 35
Female 40 14 28



What is the chi-square test-statistic for this data?
χ2=χ2=

Report all answers accurate to three decimal places.

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Expert Solution

The Expected value data are in the table below. Each Cell = Row total * Column Total/N. N = 82

Expected
Dormitory Apartment Other Total
Male 54.8374 28.6108 37.5517 121
Female 37.1626 19.3892 25.4483 82
Total 92 48 63 203

The Hypothesis:

H0: There is no relation between gender and living Arrangements.

Ha: There is a relation between gender and living Arrangements.

The Test Statistic: The table below gives the calculation of .

Number Observed Expected (O-E) (O-E)2 (O-E)2/E
1 52 54.837 -2.837 8.051 0.147
2 40 37.163 2.837 8.051 0.217
3 34 28.611 5.389 29.043 1.015
4 14 19.389 -5.389 29.043 1.498
5 35 37.552 -2.552 6.511 0.173
6 28 25.448 2.552 6.511 0.256
Total 3.306

test = 3.31

_________________________________

The degrees of freedom, df = (r – 1) * (c -1) = (3 - 1) * (2 - 1) = 2

The Critical Value:   The critical value at = 0.05, df = 2

critical = 5.992

The p value: The p value at test = 3.31, df = 2; P value = 0.1911

The Decision Rule: If test is > critical, then Reject H0.

If p value is < , Then Reject H0.

The Decision:    Since test (3.31) is < critical (5.992), We Fail to reject H0.

Since p value (0.1911) is > (0.05), We Fail To Reject H0.


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