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A test of a mean

When you test a mean and know the standard deviation, the test statistic is the deviation from the null hypothesis mean, divided by the standard error. The standard error is the standard deviation divided by the square root of the number of observations. A large sample gives a small standard error, so the same deviation becomes more surprising. The sign shows whether the sample lies above or below the null hypothesis. A one-sided test upwards is used when the alternative is that the mean is higher.

Symbols

Example

$H_0: \mu = 100$, $\sigma = 10$, $n = 25$ and $\bar x = 104$.

$Z = \dfrac{104 - 100}{10/\sqrt{25}} = \dfrac{4}{2} = 2$.

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Part of Mathematics S2: Hypothesis testing.