Answer:
(0.291, 0.376)
Step-by-step 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)
