The Census Bureau provides estimates of numbers of people in

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

Solution

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]