Sample Size for Hypothesis Testing of μ

Sample Size for Hypothesis Testing of μ

A common question when setting up a hypothesis test is concerning sample size. An example, might be: How many samples do we need to measure to determine the new process is better than the old one on average?

While this seems like a simple question, we need a bit of information before we can do the calculations. I’ve also found that the initial calculation is nearly always initiated a conversation concerning the balance of sample risks, the ability to detect a change of a certain size and the constraints concerning the number of samples.

Given Values

To do the sample size calculation for a hypothesis test for the population mean, μ, we need the following set of values:

The population variance, σ². For this type of hypothesis test, we have this value based on prior measurements.

The Type I and Type II errors represented by α and β, respectively. These allow us to quantify the desired sampling risk for this particular test.

Finally, we also need to know the difference we desire to detect, Δ. This is the amount of shift or change in the mean, μ that we would like to detect if it has indeed occurred. This is similar to the difference we use in the…