In: Statistics and Probability
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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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.