Question

Determine the limits of the 90% confidence interval for , given that n = 455; and p = 0.11.

Answer 1

Solution :

Given that,

n = 455

= 0.11

1 - = 1 - 0.11 = 0.89

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 * (((0.11 * 0.89) / 455) = 0.0241

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.11 - 0.0241 < p < 0.11 + 0.0241

0.0859 < p < 0.1341

The 90% confidence interval for the population proportion p is : ( 0.0859 , 0.1341)