Using the accompanying data below, perform a chi-square test using alpha = 0.10

Question

Using the accompanying data below, perform a chi-square test using alpha = 0.10 to determine if the proportion of "Yes" observations differs among Populations A, B, and C Click the icon to view the observed and expected frequencies. Click the icon to view an excerpt from the table of chi-square critical values. What are the null and alternative hypotheses? What is the test statistic? What is the critical value? What is the correct conclusion? Do not reject H_0. There is enough evidence to conclude that the population proportions are different. Do not reject H_0. There is not enough evidence to conclude that the population proportions are different Reject H_0. There is not enough evidence to conclude that the population proportions are different. Reject H_0. There is enough evidence to conclude that the population proportions are different.

Explanation / Answer

Doing an Expected Value Chart,          
          
14.52   18.48  
18.48   23.52  
11   14  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    5.793908472   [ANSWER, TEST STATISTIC]

**********************************  
          
With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    2      
b =    3      
          
df =    2      
          
Thus, the critical value is          
          
significance level =    0.05      
          
chi^2(critical) =    5.991464547   [ANSWER, CRITICAL VALUE]

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As chi^2 < 5.991, we   FAIL TO REJECT THE NULL HYPOTHESIS.      
          
Hence,

OPTION B. Do not reject Ho. THere is not enough evidence to conclude that the proportions are different. [ANSWER]

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