Question

If n=530 and X = 424, construct a 95% confidence interval. Give your answers to three decimals

answer ____ < p < answer _____

Answer 1

Solution :

Given that,

n = 530

x = 424

Point estimate = sample proportion = = x / n = 424 /530=0.8

1 - = 1-0.8=0.2

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =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) /530 )

E = 0.034

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.8 - 0.034< p < 0.8+0.034

0.766< p < 0.834

The 95% confidence interval for the population proportion p is : 0.766< p < 0.834