Question

You wish to estimate the population proportion of professional athletes that wear contact lenses while they play their sport. Assuming that no preliminary estimate is available, what is the minimum sample size required to be 95% confident that your estimate is in error by no more than 0.04? 1601 13 60,025 151

Answer 1

Solution :

Given that,

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

margin of error = E = 0.04

Z$\alpha$/2 = 1.96

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

= (1.96 / 0.04)2 * 0.5 * 0.5

= 601

The minimum sample size required is 601