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(√(p(1-p)))/(√(n))\\p=(297)/(1873)=0.1586\\ \hat{p}=0.1586\pm(√(0.1586(1-0.1586)))/(√(1873))\\=0.1586\pm(√(0.1586(0.8414)))/(43.2782)}\\=0.1586\pm(√(0.1334))/(43.2782)}\\=0.1586\pm(0.3653)/(43.2782)}\\=0.1586\pm0.0084`