Question

If you wish to estimate a population mean to within 0.2 using a 95% confidence interval and you know from prior sampling that $\sigma ^{2}$ is approximately equal to 5.4, how many observations would you have to include in your sample?

Thank You!

Answer 1

Solution :

Given that,

Standard deviation ($\sigma$) = $\sqrt$Variance = $\sqrt$5.4

                                 = 2.32

Margin of error = E = 0.2

Z_$\alpha$/2 = 1.96

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

n = [1.96 * 2.32/0.2]²

= 516.92

= 517

We have to include 517 observations.