Question

Confidence Interval Problem 18

Confidence Intervals: Problem 18 Previous Problem Problem List Next Problem (1 point) Chuck wants to determine a 98% confidence interval for the true proportion of times he rolls a 5 (using a fair, 6-sided die). How many rolls must Chuck make to get a margin of error less than or equal to .05? Chuck assumes that pis 1/6. n =

Answer 1

Solution :

Given that,

$\hat p$ = 1/6=0.167

1 - $\hat p$ = 1 - 0.167 = 0.833

margin of error = E = = 0.05

At 98% confidence level the z is,

Z_$\alpha$/2 = 2.326 ( Using z table  

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

= (2.326 / 0.05)² * 0.167* 0.833

=301.05

Sample size = 301