Question

In a study of perception, 80 men are tested and 7 are found to have red/green color blindness. A 99% confidence interval for this proportion would be .0875 plus or minus:

In a study of perception, 80 men are tested and 7 are found to have red/green color blindness. A 99% confidence interval for this proportion would be .0875 plus or minus 0.0813 @.0316 O .0520 ©.0619

Answer 1

Solution :

Given that,

n = 80

x = 7

Point estimate = sample proportion = $\hat p$ = x / n = 7 / 80 = 0.0875

1 - $\hat p$ = 1 - 0.0875 = 0.9125

At 99% confidence level

$\alpha$ = 1 - 99%

$\alpha$ =1 - 0.99 =0.01

$\alpha$/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)

E = 2.576 ($\sqrt$((0.0875 * 0.9125) / 80)

E = 0.0813