Question

Suppose a sociologist studying the sleep habits of teenagers in the U.S. randomly surveyed 1873 teenagers. Of those, 297 teenagers had moderate to severe sleep disorders. What would be the value of ^p? Please show me the work and how u get it because i don't understand.

Answer 1

$\hat{p}=p\pm\frac{\sqrt{p(1-p)}}{\sqrt{n}}\\p=\frac{297}{1873}=0.1586\\ \hat{p}=0.1586\pm\frac{\sqrt{0.1586(1-0.1586)}}{\sqrt{1873}}\\=0.1586\pm\frac{\sqrt{0.1586(0.8414)}}{43.2782}}\\=0.1586\pm\frac{\sqrt{0.1334}}{43.2782}}\\=0.1586\pm\frac{0.3653}{43.2782}}\\=0.1586\pm0.0084$