Question

Construct a? 95% confidence interval to estimate the population proportion using the data below.

x = 29

n = 90

N = 500

The? 95% confidence interval for the population proportion is? (_,_).

Answer 1

Solution :

Given that,

n = 90

x = 29

= x / n = 29 / 90 = 0.322

1 - = 1 - 0.322 = 0.678

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

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

= 1.96 * (((0.322 * 0.678) / 90)

= 0.096

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.322 - 0.096 < p < 0.322 + 0.096

0.226 < p < 0.418

(0.226 , 0.418)