Lecture 6 - Ch 8c - Determining Sample Size

Determining Sample Size

Up until now in this chapter, we've determined the confidence interval based on a give sample. We now ask how to determine the appropriate sample size based on a known confidence level. We ask ourselves - if we want to know the mean within a certain margin of error with a xx% confidence, how large a sample do we need to take?

Margin of Error (e) = z_alpha/2(sigma/sqrt(n))

When we know the desired margin of error ahead of time, we call it the "maximum tolerable error".

Solving the equation above for n, we get:
n = (z_alpha/2sigma/e)²

Example:
What sample size should we use if we want a 90% confidence interval with a maximum tolerable error of +/- 5 with a population that has std dev of 45?

Answer:
z_alpha/2 for 90% (alpha=0.1) is 1.645.
So, n = ((1.645)(45)/5)² = 219.19
Therefore use a sample size of 220.