Question

To estimate the mean of a normal population whose standard deviation is 36, with a margin of error equal to 3 and confidence level 95% requires a sample size of at least (report your answer in integers)

Answer 1

Solution

standard deviation = $\sigma$   =36

Margin of error = E = 3

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*36 /3 )2

n =553.1904

Sample size = n =554