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Just a note

This graph shows the theoretical probability density of a standard normally distributed population of results. Depending upon which you want to test, this population can be either your observations, or some statistic calculated from them - most commonly the latter.

In this graph the horizontal axis assumes each result has been standardised, by subtracting the population mean, then dividing by the population standard deviation. Remember that, in a Z test, you cannot substitute sample means and standard errors for their population equivalents - because they are both measured with error.