Question

If you wish to estimate a population mean with a margin of error MEequals=0.33

using a​ 95% confidence interval and you know from prior sampling that σ2

is approximately equal to 4.6 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 (______) ​(Round up to the nearest​ observation.)  

Answer 1

Answer

We have variance = 4.6

first, we need to find standard deviation

standard deviation =

Margin of error = ME = 0.33

We have to find sample size using 95% confidence interval, so z score = 1.96 (using z distributiont table)

Formula for the sample size is given as

n = $((z*sigma)/ME)^2$

setting the given values, we get

Rounding it off to next whole number, we get

sample size n = 162