Z-test is a statistical test where normal distribution is applied and is basically used for dealing with problems relating to large samples when n ≥ 30.
n = sample size
For example suppose a person wants to test if both tea & coffee are equally popular in a particular town. Then he can take a sample of size say 500 from the town out of which suppose 280 are tea drinkers. To test the hypothesis, he can use Z-test.
There are different types of Z-test each for different purpose. Some of the popular types are outlined below:
Statistically speaking, we test the null hypothesis H0: p = p0 against the alternative hypothesis H1: p >< p0 where p is the population proportion and p0 is a specific value of the population proportion we would like to test for acceptance.
The example on tea drinkers explained above requires this test. In that example, p0 = 0.5. Notice that in this particular example, proportion refers to the proportion of tea drinkers.
For example suppose one is interested to test if there is any significant difference in the habit of tea drinking between male and female citizens of a town. In such a situation, Z-test for difference of proportions can be applied.
One would have to obtain two independent samples from the town- one from males and the other from females and determine the proportion of tea drinkers in each sample in order to perform this test.
Statistically speaking, we test the null hypothesis H0: μ = μ0 against the alternative hypothesis H1: μ >< μ0 where μ is the population mean and μ0 is a specific value of the population that we would like to test for acceptance.
Unlike the t-test for single mean, this test is used if n ≥ 30 and population standard deviation is known.
Statistically speaking, we test the null hypothesis H0: σ = σ0 against H1: σ >< σ0 where σ is the population mean and σ0 is a specific value of the population variance that we would like to test for acceptance.
In other words, this test enables us to test if the given sample has been drawn from a population with specific variance σ0. Unlike the chi square test for single variance, this test is used if n ≥ 30.
Irrespective of the type of Z-test used it is assumed that the populations from which the samples are drawn are normal.