The equation we want to use is: Sample Size = (Z*σ / Margin of Error)^2
We’ll use the following example question from the ASQ Black Belt Exam.
Question: When σ = 10, what sample size is needed to specify a 95% confidence interval of ±3 units from the mean?
Step 1: Find the Z score
We need Z(α/2), where α is the confidence interval.
You would just look that up on the Z table.
In this case:
α = 95
Z(α/2) = Z(95/2) = Z(47.5) = 1.96
Step 2: Apply the Equation Sample Size = (Z*σ / Margin of Error)^2
Just a simple plug and play equation:
Sample Size = (Z*σ / Margin of Error)^2 = (1.96 * 10 / 3)^2 = (19.6/3)^2 = 6.53^2 = 42.7