Question

(1 point) Find the size of the sample needed to estimate the difference between the proportions of boys and girls under 10 years old who are afraid of spiders. Assume that we want 99% confidence that the error is smaller than 0.07. n=

Answer 1

Solution :

Given that,

$\hat p$ = 1 - $\hat p$ = 0.5

margin of error = E = 0.07

Z_$\alpha$/2 = 2.576

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

= (2.576 / 0.07)² * 0.5 * 0.5

= 339

sample size = n = 339