Question

When 480 college students were surveyed, 160 said they own a car. Construct a 95% confidence interval for the proportion of college students who say they own a car.

Answer 1

(0.291, 0.376)

Explanation:

Confidence interval = mean or proportion ± margin of error

CI = μ or p ± ME

The proportion is p = 160/480 = 0.333.

Margin of error = critical value × standard error

For 95% confidence, CV = 1.960 (from t table).

Standard error for a proportion is √(pq / n), where n is the sample size, p is the proportion, and q is 1−p.

Solving for margin of error:

ME = 1.960 √(0.333 × 0.667 / 480)

ME = 0.042

The confidence interval is:

CI = 0.333 ± 0.042

(0.291, 0.376)