Z-tests are crucial statistical procedures to test for claims about population parameters using the normal distribution.

Z-tests, as all parametric tests, require certain distributional assumptions to be met. As with anything in Statistics, we need to look for signs to assess whether it is likely not that the distributional assumptions are met.

Typically, a Z-test will require the underlying distribution to be normally distributed, but such assumption can be typically be relaxed when the sample size is large enough, by virtue of the Central Limit Theorem.

### Applications of Z-tests

We can use for one population or two population means provided that the population standard deviations are known. Also, we can use a z-test to test for claims about a population proportion.

Also, via the Central Limit Theorem (CLT), the z-test can be used as an approximation by many statistical procedures (parametric and non-parametric).

In this page you will all the Z-tests we have available. Check the list below:

## Z-test for One Population Mean

Instructions: This calculator conducts a Z-test for one population mean ((mu)), with known population standard deviation ((sigma)). Please select the null and alternative hypotheses, type the hypothesized mean, the significance level, the sample ...

## Z-test: One Population Proportion

Instructions: This calculator conducts a Z-test for one population proportion (p). Please select the null and alternative hypotheses, type the hypothesized population proportion (p_0), the significance level (alpha), the sample proportion (or ...

## Z-test for two Means, with Known Population Standard Deviations

Instructions: This calculator conducts a Z-test for two population means ((mu_1) and (mu_2)), with known population standard deviations ( (sigma_1) and (sigma_2)). Please select the null and alternative hypotheses, type the significance level, the ...

## Z-test for Two Proportions

Instructions: This calculator conducts a Z-test for two population proportions ((p_1) and (p_2)), Please select the null and alternative hypotheses, type the significance level, the sample sizes, the number of favorable cases (or the sample ...

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