Question

f n=450 and p' (p-prime) = 0.06, construct a 99% confidence interval.

Give your answers to three decimals.

< p <

Answer 1

Solution :

Given that,

n = 450

$\hat p$ =0.06

1 -$\hat p$ = 1 - 0.06 = 0.94

At 99% confidence level the z is ,

$\alpha$  = 1 - 99% = 1 - 0.99 = 0.01

$\alpha$ / 2 = 0.01 / 2 = 0.005

Z_$\alpha$/2 = Z_0.005 = 2.576

Margin of error = E = Z_{$\alpha$ / 2} * $\sqrt$(($\hat p$ * (1 - $\hat p$ )) / n)

= 2.576 * ($\sqrt$((0.06 * 0.94) / 450) = 0.029

A 99 % confidence interval for population proportion p is ,

$\hat p$ - E < P <$\hat p$ + E

0.06 - 0.029 < p < 0.06 + 0.029

0.031< p < 0.089

The 99% confidence interval for the population proportion p is : ( 0.031< p < 0.089)