The accompanying table summarizes data for a sample of women. Using a 0.10 signi

Question

The accompanying table summarizes data for a sample of women. Using a 0.10 significance level, test the claim that the proportion of agree/disagree responses are the same for the subjects interviewed by either gender. Does it appear that the gender of the interviewer affected the responses of women? Does it appear that the gender of the interviewer affected the responses? No, the null hypothesis of homogeneity is rejected. Yes, the null hypothesis of homogeneity is rejected. No, the null hypothesis of homogeneity is not rejected. Yes, the null hypothesis of homogeneity is not rejected.

Explanation / Answer

Doing an Expected Value Chart,          
          
410   390
205   195
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    10.14634146      
          
With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    2      
b =    2      
          
df =    1      
          
Thus, the critical value is          
          
significance level =    0.1      
          
chi^2(critical) =    2.705543454      
          
Also, the p value is          
          
P =    0.001445879      
          
As chi^2 > 2.706, and P < 0.10, we   REJECT THE NULL HYPOTHESIS.      
          
Thus, there is significant evidence that the gender of the interviewer affected the responses at 0.01 level.

[OPTION B, ANSWER]

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