A recent survey showed that 63 of US employers were likely t

A recent survey showed that 63% of U.S. employers were likely to require higher employee contributions for health care coverage. Suppose the survey was based on a sample of 700 companies. Find the 90% confidence interval for the proportion of all companies likely to require higher employee contributions for health care coverage.

Q1. What is left endpoint

Q2. What is right endpoint

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.63          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.018248288          
              
Now, for the critical z,              
alpha/2 =   0.05          
Thus, z(alpha/2) =    2.33          
Thus,              
              
lower bound = p^ - z(alpha/2) * sp =   0.58748149 [ANSWER, LEFT ENDPOINT]
          
upper bound = p^ + z(alpha/2) * sp =    0.67251851   [ANSWER, RIGHT ENDPOINT]