Question

In a random sample of 200 Vancouverites, 34.5% received the flu vaccination in the past year. You would like to calculate a 99% confidence interval. What sample size is needed for the margin of error to be at most 5%? Answer as a whole number.

Answer 1

Solution :

Given that,

$\hat p$= 0.345

1 - $\hat p$ = 1 - 0.345 = 0.655

margin of error = E = 5% = 0.05

At 99% confidence level the z is,

$\alpha$ = 1 - 99%

$\alpha$ = 1 - 0.99 = 0.01

$\alpha$/2 = 0.005

Z_$\alpha$/2 = 2.576

Sample size = n = (Z_$\alpha$/2 / E)² * $\hat p$ * (1 - $\hat p$ )

= (2.576 / 0.05)² * 0.345 * 0.655

=599.8077

Sample size = 600