Question

When 490 college students were surveyed, 130 said they own their car. Construct a 95%

confidence interval for the proportion of college students who say they own their cars.

Answer 1

0.2454 ≤ x ≤ 0.2852

Step-by-step explanation:

Given the following parameters:

Number of students = 410

Number of students that own their cars = 130

Hence we have Proportion of those who own a car (P) = 130/490 = 0.2653

Thereby, at 95% confidence, Z = 1.96

Sample size is represented as N = 490

Confidence interval = P+/- Z * Sqrt (P (1-P) / N)

=> 0.2653 +/- 1.96 * Sqrt (0.265 (1-0.265) / 490)

=> 0.2653 +/- 0.0199

Therefore, for any randomly selected student (y), the probability that he/she owns a car is;

0.2454 ≤ x ≤ 0.2852