# Why should I use a 1-sample Z test?

To perform this test, select Stat > Basic Statistics > 1-Sample Z.

Use the 1-sample Z-test to estimate the mean of a population and compare it to a target or reference value when you know the standard deviation of the population. Using this test, you can:
• Determine whether the mean of a group differs from a specified value.
• Calculate a range of values that is likely to include the population mean.

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 Stat > Basic Statistics > 1-Sample t.

For 1-Sample Z, the hypotheses are:
Null hypothesis
 H0: μ = µ0 The population mean (μ) equals the hypothesized mean (µ0).
Alternative hypothesis
Choose one:
 H1: μ ≠ µ0 The population mean (μ) differs from the hypothesized mean (µ0). H1: μ > µ0 The population mean (μ) is greater than the hypothesized mean (µ0). H1: μ < µ0 The population mean (μ) is less than the hypothesized mean (µ0).
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