Question

B. Religion and 2008 Presidential Vote

	Obama	McCain	TOTAL
Catholic	290	185	475
Protestant	300	450	750
Other	175	50	225
TOTAL	765	685	1450

1. Reproduce the table using column percentages

2. Reproduce the table using row percentages
   

3. Reproduce the table using total percentages

4. Is there a clear independent variable; which variables is it?

5. What is the null hypotheses?

6. Compute the Chi-square; is the association significant (careful computing df and finding critical value)?

7. Interpret the association

Answer 1

a)

based on column percentage
	Obama	McCain	Total
Catholic	37.9%	27.0%	32.8%
Protestant	39.2%	65.7%	51.7%
Other	22.9%	7.3%	15.5%
Total	100.0%	100.0%	100.0%

b)

based on row percentage
	Obama	McCain	Total
Catholic	61.1%	38.9%	100.0%
Protestant	40.0%	60.0%	100.0%
Other	77.8%	22.2%	100.0%
Total	52.8%	47.2%	100.0%

c)

based on total percentage
	Obama	McCain	Total
Catholic	20.0%	12.8%	32.8%
Protestant	20.7%	31.0%	51.7%
Other	12.1%	3.4%	15.5%
Total	52.8%	47.2%	100.0%

d) 2008 presidential vote

e) Ho: Religion and 2008 Presidential Vote ar not associated

f)

Chi-Square Test of independence
	Observed Frequencies
	Obama	McCain					Total
Catholic	290	185					475
Protestant	300	450					750
Other	175	50					225
Total	765	685					1450
	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	Obama	McCain					Total
Catholic	765*475/1450=250.603	685*475/1450=224.397					475
Protestant	765*750/1450=395.69	685*750/1450=354.31					750
Other	765*225/1450=118.707	685*225/1450=106.293					225
Total	765	685					1450
	(fo-fe)^2/fe
Catholic	6.1934	6.9167
Protestant	23.1406	25.8432
Other	26.6953	29.8130

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   118.6022  
      
Level of Significance =   0.05  
Number of Rows =   3  
Number of Columns =   2  
Degrees of Freedom=(#row - 1)(#column -1) = (3- 1 ) * ( 2- 1 ) =   2  
      

Critical Value =   5.991   [ Excel function: =CHISQ.INV.RT(α,DF) ]
Decision: test stat,X² > critical value , So, Reject the null hypothesis      

conclusion: Religion and 2008 Presidential Vote are associated

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g) interpret: there is enough evidence to conclude that Religion and 2008 Presidential Vote are associated