Question

If n=600 and X = 480, construct a 95% confidence interval. Give your answers to three decimals

< p

Answer 1

Solution :

Given that,

n = 600

x = 480

Point estimate = sample proportion = = x / n = 480 /600=0.8

1 -   = 0.2

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   ( Using z table )

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

= 1.96 (((0.8*0.2) /600 )

E = 0.032

A 95% confidence interval for population proportion p is ,

- E < p

0.8-0.032 <p

0.768<p