Question

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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Answer 1

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.