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.

image1 - chi-square test formula
image1 – chi-square test formula

where:

  • N is the total number of observation of the two sample;
  • S1 and S2 are the standard deviation of the two saple.


It’s important to remember that now we are working with the Chi-square distribution, and to find the critical value, at some degree of freedom and alpha level, we need to use the Chi-square table.

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