A recent survey showed that 59 of US employers were likely t

A recent survey showed that 59% of U.S. employers were likely to require higher employee contributions for health care coverage. Suppose the survey was based on a sample of 600 companies. Find the 99% confidence interval for the proportion of all companies likely to require higher employee contributions for health care coverage. Find left end point and right end point. 4 decimal place values.

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.59          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.020079011          
              
Now, for the critical z,              
alpha/2 =   0.005          
Thus, z(alpha/2) =    2.33          
Thus,              
              
left endpoint = p^ - z(alpha/2) * sp =   0.5432   
right endpoint = p^ + z(alpha/2) * sp =    0.6368
              
Thus, the confidence interval is              
              
(   0.5432   ,   0.6368   ) [ANSWER]