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Different hypothesis tests make different assumptions about the distribution of the random variable being sampled in the data. These assumptions must be considered when choosing a test and when interpreting the results.

For example, the * z*-test (

`ztest`

) and the `ttest`

) both assume that the
data are independently sampled from a normal distribution. Statistics and Machine Learning Toolbox™ functions
are available for testing this assumption, such as `chi2gof`

, `jbtest`

, `lillietest`

, and `normplot`

.Both the * z*-test and the

The difference between the * z*-test and the

Test statistics for the * z*-test and the

$$\begin{array}{l}z=\frac{\overline{x}-\mu}{\sigma /\sqrt{n}}\\ t=\frac{\overline{x}-\mu}{s/\sqrt{n}}\end{array}$$

Under the null hypothesis that the population is distributed
with mean * μ*, the

Knowing the distribution of the test statistic under the null
hypothesis allows for accurate calculation of * p*-values.
Interpreting

Assumptions underlying Statistics and Machine Learning Toolbox hypothesis tests are given in the reference pages for implementing functions.

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