In a survey, 29% of 230 single women said that they \"definitely want to get mar

Question

In a survey, 29% of 230 single women said that they "definitely want to get married." In the same survey, 22% of 285 single men gave the same response. Construct a 99% confidence interval estimate of the difference between the proportions of single women and single men who definitely want to get married. Is there a gender gap? Construct a 99% confidence interval estimate. Is there a gender gap? Choose the correct answer below. Since the interval does not contain 0, there is no evidence of a gender gap. Since the interval does not contain 0, there is evidence of a gender gap. Since the interval contains 0, there is no evidence of a gender gap. Since the interval contains 0, there is evidence of a gender gap.

Explanation / Answer

          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.29      
p2 = x2/n2 =    0.22      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.038695254      
          
For the   99%   confidence level, then  
          
alpha/2 = (1 - confidence level)/2 =    0.005      
z(alpha/2) =    2.575829304      
Margin of error = z(alpha/2)*sd =    0.099672368      
lower bound = p1^ - p2^ - z(alpha/2) * sd =    -0.029672368      
upper bound = p1^ - p2^ + z(alpha/2) * sd =    0.169672368      
          
Thus, the confidence interval is          
          
(   -0.029672368   ,   0.169672368 ) [ANSWER]

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As we can see, 0 is inside the interval, so

OPTION C: Since the interval contains 0, there is no evidence of a gender gap. [ANSWER]

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