Question

You want to estimate the mean IQ for a population of students with a 95% confidence interval. Assume that the population standard deviation is known to be 15. If you want your estimate to be within 5 points of the value of the parameter, you will need a sample size of... (Round z to the nearest hundredth.)

Answer 1

Solution

standard deviation =s = $\sigma$   =15

Margin of error = E = 5

At 95% confidence level the z is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

$\alpha$ / 2 = 0.05 / 2 = 0.025

Z$\alpha$/2 = Z0.025 = 1.96

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

n = ( 1.96*15 /5 )2

n =34.57

Sample size = n =35