Question

A study was done by researchers at a University to determine the percentage of all student athletes in the U.S. that have been subjected from bullying. The study found 805 student athletes reported being bullied out of 1400. Baded on this sample, construct a 95% confidence interval for the proportion of all student athletes that have been bullied. Interpret your confidence interval in words.

Answer 1

Solution :

Given that,

n = 1400

x = 805

Point estimate = sample proportion = = x / n = 805/1400=0.575

1 -   = 1- 0.575 =0.425

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.575*0.425) / 1400)

E = 0.026

A 95% confidence interval for proportion p is ,

- E < p < + E

0.575-0.026 < p < 0.575+0.026

(0.549 , 0.601)