A sample of 250 people resulted in a confidence interval est

A sample of 250 people resulted in a confidence interval estimate of between 0.14 and 0.20 for the proportion of people who believe that the federal government\'s proposed tax increase is justified. Based on this information, what was the confidence level used in this estimation?

Solution

As

Margin of error = (upper-lower)/2 = (0.20-0.14)/2 = 0.03

and

p^ = (upper+lower)/2 = 0.17

Getting the standard error of p^, sp,          
          
sp = sqrt[p^ (1 - p^)/n] =    0.023757104      
          

Then

z = E/sp = 0.03/0.023757104 = 1.262780177

Hence, getting the right tailed area,

alpha/2 = 0.103334095

Thus,

c = 1 - alpha = 0.793331809 [or probably, 80% confidence] [ANSWER]