The Census Bureau provides estimates of numbers of people in the USA classified
ID: 3024306 • Letter: T
Question
The Census Bureau provides estimates of numbers of people in the USA classified in various ways. Let’s look at college students. The following table gives us data to examine the relation between gender and full time or part time status for 20 to 24 age category. Perform the significance test to determine if there is a relationship between this two variables. Give the test statistic and P-value.
Gender
Total
Status
Male
Female
Full-time
2719
2991
5710
Part-time
535
680
1215
Total
3254
3671
6925
Gender
Total
Status
Male
Female
Full-time
2719
2991
5710
Part-time
535
680
1215
Total
3254
3671
6925
Explanation / Answer
Doing an Expected Value Chart,
2683.081588 3026.918412
570.9184116 644.0815884
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 5.169865666 [ANSWER, TEST STATISTIC]
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With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,
a = 2
b = 2
df = 1
Thus, the p value is
P = 0.022981993 [ANSWER]
As P < 0.05, we REJECT THE NULL HYPOTHESIS.
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Thus, there is significant evidence that gender and full-time or part-time status are not independent at 0.05 level. [CONCLUSION]
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