Quick Lube is interested in the proportion of customers who

Quick Lube is interested in the proportion of customers who return after receiving a reminder card for an oil change. In a random sample of 100 customers, 62 returned with a month. For a 95% confidence interval on the proportion of customers who return for an oil change,

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.62          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.048538644          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
              
lower bound = p^ - z(alpha/2) * sp =   0.524866005          
upper bound = p^ + z(alpha/2) * sp =    0.715133995          
              
Thus, the confidence interval is              
              
(   0.524866005   ,   0.715133995   ) [ANSWER]