Use the given degree of confidence and sample data to constr

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. Round to three decimal places.

When 343 college students are randomly selected and surveyed, it is found that 110 own a car. Find a 99% confidence interval for the true proportion of all college students who own a car.

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.320699708          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.025201891          
              
Now, for the critical z,              
alpha/2 =   0.005          
Thus, z(alpha/2) =    2.575829304          
Thus,              
Margin of error = z(alpha/2)*sp =    0.064915768          
lower bound = p^ - z(alpha/2) * sp =   0.25578394          
upper bound = p^ + z(alpha/2) * sp =    0.385615477          
              
Thus, the confidence interval is              
              
(   0.25578394   ,   0.385615477   ) [ANSWER]