The One-sample variance hypothesis test is a parametric test, also called the Chi-square hypothesis test. It can be used to test if the variance of a population is equal to a specified value.

For this test you need to know:

• The size and the standard deviation of the sample;
• The target standard deviation for the pouplation.

It’s important to know that:

The hypothesis of this test is like this in case of the two tails test:

• H0: V1 = V2 that means that the sample1 variance are equal to the target variance;
• H1V1 != V2 that means that the sample1 variance and the target variance are different

In case of one tails left you can have for example:

• H0: V1 = V2 that means that the sample1 variance is higher or equal than the target vairance;
• H1V1 < V2 that means that the sample1 variance are lower than the target variance.

In case of one tails rightyou can have for example:

• H0: V1 = V2 that means that the sample1 variance is higher or equal than the target vairance;
• H1V1 > V2 that means that the sample1 variance are lower than the target variance.

The way to conduct the hypothesis test is like the one-sample t-tests, but we use the statistics formula in the image1.