Question

Both before and after a recent earthquake, surveys were conducted asking voters which of the three candidates they planned on voting for in the upcoming city council election. Has here been a change since the earthquake? You are conducting a Test of Independence for the claim that there is an association between the earthquake and the voter support at α=0.05α=0.05. The following table summarize the result of the survey.

	Perez	Chung	Stevens
Before	38	27	37
After	22	17	27

1. For this study, we should use Select an answer 1-PropZTest 1-PropZInt 2-PropZInt χ²GOF-Test 2-SampTInt ANOVA 2-SampTTest χ²-Test T-Test TInterval 2-PropZTest
2. 
   
3. Your friend Brittany helped you with the null and alternative hypotheses...
   H0:H0: The votor support is independent from the earthquake
   H1:H1: There is an association between the earthquake and the voter support
   The expected observations for this table would be (Please show your answers to 1 decimal place)

   	Perez	Chung	Stevens
   Before
   After

4. 
   
5. 
   
6. 
   
7. The test-statistic for this data =  (Please show your answer to 3 decimal places.)
8. 
   
9. The p-value for this sample =  (Please show your answer to 4 decimal places.)
10. 
    
11. The p-value is Select an answer less than (or equal to) alpha greater than alpha  αα
12. 
    
13. Base on this, we should Select an answer accept the alternative hypothesis accept the null hypothesis fail to reject the null hypothesis reject the null hypothesis  hypothesis
14. 
    
15. As such, the final conclusion is that...
    • The sample data suggests there is not sufficient evidence to conclude the claim that there is an association between the earthquake and the voter support at α=0.05α=0.05.
    • The sample data suggests there is sufficient evidence to conclude the claim that there is an association between the earthquake and the voter support at α=0.05α=0.05.

Answer 1

χ²-Test for independence

below is expected value table:

Expected	Ei=row total*column total/grand total	Perez	Chung	Stevens
	before	36.4	26.7	38.9
	after	23.6	17.3	25.1

Applying chi square test of independence:

chi square    χ2	=(Oi-Ei)2/Ei	Perez	Chung	Stevens	Total
	before	0.068	0.003	0.089	0.1596
	after	0.105	0.0047	0.1372	0.2467
	total	0.1725	0.0078	0.2259	0.406
test statistic X2 =	0.406

The p-value for this sample = 0.8162

The p-value is greater than alpha

fail to reject the null hypothesis

The sample data suggests there is not sufficient evidence to conclude the claim that there is an association between the earthquake and the voter support at α=0.05