Question

Given n =1000, x = 841, Find a 95% confidence interval for the proportion 841/1000
=.841

Answer 1

Solution :

Given that,

n = 1000

x = 841

Point estimate = sample proportion = = x / n = 0.841

1 -   = 0.159

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 (((0.841*0.159) / 1000)

E = 0.023

A 95% confidence interval is ,

- E < p < + E

0.841-0.023 < p < 0.841 +0.023

(0.818 , 0.864)