The research group asked the following question of individuals who earned in exc

Question

The research group asked the following question of individuals who earned in excess of $100,000 per year and those who earned less than $ 100,000 per year *Do you believe that it is morally wrong for unwed women to have children?" of the 1, 205 individuals who earned in excess of $100,000 per year 715 said yes. of the 1,310 individuals who earned less than $100,000 per year 700 said yes Construct a 95% confidence interval to determine if there is a difference in the proportion of individuals who believe it is morally wrong for unwed women to have children

Explanation / Answer

Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.593360996      
p2 = x2/n2 =    0.534351145      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.019752832      
For the   95%   confidence level, then  
          
alpha/2 = (1 - confidence level)/2 =    0.025      
z(alpha/2) =    1.959963985      
Margin of error = z(alpha/2)*sd =    0.03871484      
lower bound = p1^ - p2^ - z(alpha/2) * sd =    0.020295011      
upper bound = p1^ - p2^ + z(alpha/2) * sd =    0.097724691      
          
Thus, the confidence interval is          
          
(   0.020   ,   0.098 ) [ANSWER]

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