Question

In a sample of 300 students, 68% said they own an iPod and a smart phone. Compute a 95% confidence interval for the true percent of students who own an iPod and a smartphone.

Answer 1

$p=0.68 \\ q=1-p=1-0.68=0.32 \\ CI \; 0.95 \\ α=1-0.95=0.05 \\ \frac{α}{2}=0.025 \\ Z_{0.025}=1.959 \\ CI = p ±Z_{0.025} \sqrt{\frac{pq}{n}} \\ = 0.68 ± 1.959 \times \sqrt{\frac{0.68 \times 0.32}{300}} \\ = 0.68 ±0.052$

CI: 0.628 ≤ p ≤0.732