Shortly after September 11th 2001 a researcher wanted to det

Shortly after September 11th 2001, a researcher wanted to determine if the proportion of females that favored war with Iraq was significantly different from the proportion of males that favored war with Iraq. In a sample of 74 females, 30 favored war with Iraq. In a sample of 52 males, 34 favored war with Iraq.

e) What is the lower endpoint of a 99% confidence interval for the difference between the proportion of females that favor the war and the proportion of males that favor the war? Give your answer to four decimal places.

f) What is the upper endpoint of a 99% confidence interval for the difference between the proportion of females that favor the war and the proportion of males that favor the war? Give your answer to four decimal places.

Solution

Let p1 = proportion of females
p2 = proportion of males

E)

Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.405405405      
p2 = x2/n2 =    0.653846154      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.087235221      
          
  
          
For the   99% lower confidence level, then  
          
alpha = (1 - confidence level) =    0.01      

z(alpha) =    2.326347874      

Thus,
          
lower bound = p1^ - p2^ - z(alpha) * sd   = -0.451380219 = 0.4514 [ANSWER]  

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F)

Also,   

upper bound = p1^ - p2^ + z(alpha) * sd   = -0.045501278   [ANSWER]