Question

If n = 140 and X = 112, construct a 99% confidence interval for the population proportion, p. Give your answers to three decimals

< p

Answer 1

Solution :

Given that,

n = 140

x = 112

Point estimate = sample proportion = = x / n = 112 / 140=0.8

1 -   = 1- 0.8 =0.2

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z  0.005 = 2.576 ( Using z table )

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

= 2.576* (((0.8*0.2) /140 )

E = 0.087

A 99% confidence interval is ,

- E < p

0.8 - 0.087< p

0.713< p