Statistics Z Test

A Z-test is a statistical hypothesis test that is used to determine whether a sample mean is significantly different from a population mean. It assumes that the data being tested is approximately normally distributed.

In a Z-test, the sample mean is standardized by subtracting the population mean and dividing by the standard deviation of the population. The resulting standardized value is called the Z-score.

The Z-test provides a test statistic, which can be used to make decisions about the null hypothesis, which is usually that the sample mean is equal to the population mean. If the test statistic falls outside of a certain range, determined by a critical value, it is evidence against the null hypothesis and supports the alternative hypothesis, which is usually that the sample mean is not equal to the population mean.

Z-tests are often used for hypothesis testing and to estimate confidence intervals for population parameters, such as the mean and standard deviation. They are useful when the population standard deviation is known or when the sample size is large, as the central limit theorem states that the distribution of the sample mean approaches normality as the sample size increases.