Question

Please show work. Thank you.

6. Find the minimum sample size required in to construct an 85% confidence interval about the population proportion p of college students who have a tattoo. The wanted error needs to be within 3% of the population proportion. Use the fact that 4 years ago, 11.2% of college students had a tattoo.

Answer 1

Solution :

Given that,

$\hat p$ = 0.112

1 - $\hat p$ = 1 - 0.112 = 0.888

margin of error = E = 0.03

Z_$\alpha$/2 = 1.44

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

= (1.44 / 0.03)² * 0.112 * 0.888

= 230

sample size = 230