Question

A study done by researchers at a university concluded that 90​% of all student athletes in a country have been subjected to some form of hazing. The study is based on responses from 1700 athletes. What is the margin of error and the​ 95% confidence interval for the​ study?

Answer 1

Solution :

Given that,

n = 1700

Point estimate = sample proportion = = 0.90

1 - = 0.10

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 * (((0.90 * 0.10) / 1700)

= 0.014

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.90 - 0.014 < p < 0.90 + 0.014

0.886 < p < 0.914