Example:

Finding the Smallest Sample Size Needed for a Given Margin of Error and Confidence

Suppose you want to determine the mean distance between to cells inside the human body. The margin of error (E) in this case is .01 micrometers. The population standard deviation is known to be .16 micrometers. Determine the minimum sample size required to estimate the population mean with the given error and a 95% confidence.

ANSWER:

Here, we want to calculate the smallest sample size we will need to create a 95% confidence interval (CI) with a margin of error (E) of .01.

The formula is:

n = [(zc*s)/E]²

The “s” is the standard deviation. The “E” is the desired margin of error. The zc is the critical value from the ztable for a 95% CI.

HOW TO FIND a Critical Value using the z-table

The “n” is the smallest sample size that will give us this error using this CI.

The zc can be estimated with the number  “2” because the actual z-table critical values for 95% CI is 1.96.

Answer:   Sample size “n” = [(2*.16)/(.01)] ² = 32² = 1024

NOTICE

You can estimate the sample size using 1/E^2

You must calculate E to do this

HOW TO Calculate E for Means and a Given Confidence Interval