Question

When 269 college students are randomly selected and surveyed, it is found that 116 own a car. Find a 99% confidence interval for the true proportion of all college students who own a car.

a. 0.353 < p < 0.509
b. 0.372 < p < 0.490
c. 0.361 < p < 0.502
d. 0.382 < p < 0.481

Answer 1

To find a 99% confidence interval for the true proportion of all college students who own a car, we can use the formula CI = p ± z * sqrt((p*(1-p))/n), where p is the sample proportion, z is the z-score corresponding to the desired confidence level, and n is the sample size.

Step-by-step explanation:

To find a 99% confidence interval for the true proportion of all college students who own a car, we can use the formula:

CI = p ± z * sqrt((p*(1-p))/n)

Where:

• p is the sample proportion (116/269)
• z is the z-score corresponding to the desired confidence level (99% confidence level corresponds to a z-score of 2.576)
• n is the sample size (269)

Using these values, we can calculate the confidence interval:

CI = (116/269) ± 2.576 * sqrt(((116/269)*(1-(116/269)))/269)

Calculating this gives us a confidence interval of approximately 0.353 to 0.509. Therefore, the correct answer is a. 0.353 < p < 0.509.