Question

Assume that a sample is used to estimate a population proportion. Find the 90.0% confidence interval for a sample of size 143 with 73 successes.
Give your answers as decimals, to 2 decimal places.

Answer 1

Solution :

Given that,

n = 143

x = 73

Point estimate = sample proportion = = x / n = 73/143=0.510

1 -   = 1- 0.510 =0.490

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= 1.645 *((0.510*0.490) /143 )

E= 0.07

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.510-0.07 < p <0.510+ 0.07

0.440< p < 0.580

The 90% confidence interval for the population proportion p is : 0.440, 0.580