Question

If you wish to estimate a population mean with a sampling distribution error SE=0.28 using a​ 95% confidence interval and you know from prior sampling that sigma squared is approximately equal to 3.3​, how many observations would have to be included in your​ sample?

The number of observations that would have to be included in your sample is _

Answer 1

Solution

standard deviation =s =   =3.3

Margin of error = E = 0.28

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

sample size = n = [Z/2* / E] 2

n = ( 1.96*3.3 /0.28 )2

n =533.61

Sample size = n =534