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	27	40	21
After	19	38	30

1. For this study, we should use Select an answer χ²-Test ANOVA 2-PropZTest 1-PropZInt 1-PropZTest 2-SampTInt χ²GOF-Test 2-PropZInt 2-SampTTest T-Test TInterval
2. 
   
3. Your friend Emily 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 greater than alpha less than (or equal to) alpha  αα
12. 
    
13. Base on this, we should Select an answer reject the null hypothesis fail to reject the null hypothesis accept the alternative hypothesis accept the null hypothesis  hypothesis
14. 
    
15. As such, the final conclusion is that...
    • 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.
    • 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

Answer 1

** The expected observations for this table would be

	Perez	Chung	Stevens
Before	23.1	39.2	25.6
After	22.9	38.8	25.4

** The test-statistic for this data = 3.025

** The p-value for this sample = 0.2203

** The p-value is greater than α.

** Based on this, we should fail to reject the null hypothesis.

** 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=0.05

>> Software Outputs:

Actual Values:
27 40 21
19 38 30

Expected Values:
23.1314 39.2229 25.6457
22.8686 38.7771 25.3543

Chi-Squared Values:
0.646992 0.0153979 0.84157
0.654428 0.0155749 0.851243

Chi-Square = 3.02521

Degrees of Freedom = 2

P-value = 0.220336