Question

Construct a confidence interval of the population proportion at the given level of confidence. x =120​, n =1100​, 90​% confidence

Answer 1

Solution :

Given that,

n = 1100

x = 120

Point estimate = sample proportion = = x / n = 0.109

1 - = 0.891

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z _0.05 = 1.645

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

= 1.645 * (((0.109*0.891) / 1100)

= 0.015

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.109 - 0.015 < p < 0.109 + 0.015

0.094 < p < 0.124

The 95% confidence interval for the population proportion p is :( 0.094 , 0.124 )