To perform this test, select
.For example, you take a sample of pencil stock and you want to know if the machine that cuts them to length has drifted from its intended settings.
This procedure is based on the normal distribution. So for small samples, this procedure works best if your data were drawn from a normal distribution or one that is close to normal. Because of the central limit theorem, you can use this procedure if you have a large sample, substituting the sample standard deviation for σ. Usually, you can consider samples of size 30 or higher to be large samples. If you don't know the population standard deviation, use
.H_{0}: μ = µ_{0} | The population mean (μ) equals the hypothesized mean (µ_{0}). |
H_{1}: μ ≠ µ_{0} | The population mean (μ) differs from the hypothesized mean (µ_{0}). |
H_{1}: μ > µ_{0} | The population mean (μ) is greater than the hypothesized mean (µ_{0}). |
H_{1}: μ < µ_{0} | The population mean (μ) is less than the hypothesized mean (µ_{0}). |