Question

You want to discover whether university makes students more or less politically engaged. You survey 60 students (32 freshmen and 28 seniors) and ask them whether or not they voted in the most recent state election. The results are shown in the table below.

	did not vote	voted
Freshmen	16	16
Seniors	4	24

Calculate the appropriate statistical test of your hypothesis, including test statistic, and degrees of freedom. State your conclusion regarding the research question.

Answer 1

0	did not	vote					Total
freshman	16	16					32
senior	4	24					28
Total	20	40					60
	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	did not	vote					Total
freshman	20*32/60=10.667	40*32/60=21.333					32
senior	20*28/60=9.333	40*28/60=18.667					28
Total	20	40					60
	(fo-fe)^2/fe
freshman	2.6667	1.3333
senior	3.0476	1.5238

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   8.571  
      
Level of Significance =   0.05  
Number of Rows =   2  
Number of Columns =   2  
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 2- 1 ) =   1  
      
p-Value =   0.0034148   [Excel function: =CHISQ.DIST.RT(χ²,df) ]
Decision:    p-value < α , Reject Ho