When 293 college students are randomly selected and surveyed, it is found that 114 own a car. Construct a 99% confidence interval for the true proportion of all college students who own a car. Round your answer to 3 decimal places.

The 99% confidence interval for the true proportion of all college students who own a car is (0.315, 0.463).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the z-score that has a p-value of .

When 293 college students are randomly selected and surveyed, it is found that 114 own a car.

This means that

99% confidence level

So , z is the value of Z that has a p-value of , so .

The lower limit of this interval is:

The upper limit of this interval is:

The 99% confidence interval for the true proportion of all college students who own a car is (0.315, 0.463).