Two random samples are taken with each group asked if they s

Two random samples are taken, with each group asked if they support a particular candidate. A summary of the sample sizes and proportions of each group answering yes\'\' are given below:

Pop. 1:Pop. 2:n1=88,n2=95,p^1=0.762p^2=0.693

Suppose that the data yields (-0.0553, 0.1933) for a confidence interval for the differencep1p2 of the population proportions. What is the confidence level? (Give your answer in terms of percentages.)

Confidence Level =  %.

I got 97.06 as a answer, what am I doing wrong?

Solution

Here, the margin of error is

E = (0.1933 - (-0.0553))/2 = 0.1243

Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.762      
p2 = x2/n2 =    0.693      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.065577037      
          
Thus,

zcrit = E/sd = 0.1243/0.065577037 = 1.895480578

Thus, getting one tailed area for this,

alpha/2 = 0.029014381

Thus,

alpha = 0.058028762

confidence level = 1 - alpha = 0.941971238 or 94.2% [ANSWER]