Question

It is known that the population standard deviation for the IQ test is 14. What sample size would be needed to collect in order to calculate a 95% CI for the mean that is within 0.08 points? What sample size would be needed to collect in order to calculate a 98% CI for the mean that is within 1 point?

Answer 1

Solution :

4.

Given that,

standard deviation =  $\sigma$ =14

Margin of error = E = 0.08

At 95% confidence level the z is,

$\alpha$ = 1 - 95%

$\alpha$ = 1 - 0.95 = 0.05

$\alpha$/2 = 0.025

Z_$\alpha$/2 = 1.96

sample size = n = [Z_$\alpha$/2* $\sigma$ / E] ²

n = [ 1.96* 14/ 0.08]²

n =117649

Sample size = n =117649

5.

Solution :

Given that,

standard deviation =  $\sigma$ =14

Margin of error = E = 1

At 98% confidence level the z is,

$\alpha$ = 1 - 98%

$\alpha$ = 1 - 0.98 = 0.02

$\alpha$/2 = 0.01

Z_$\alpha$/2 = 2.326

sample size = n = [Z_$\alpha$/2* $\sigma$ / E] ²

n = [ 2.326* 14/ 0.01]²

n =10604140.96

Sample size = n =10604141