How do we conduct a formal hypothesis test of a claim made about two population standard deviations or variances.

Given:

Standard deviation or variance of two population.

We need to write a method by which a formal hypothesis test can be conducted of claim made about two population standard deviations or variances.

In General Chi-Square test and F-test are used for variance or standard deviation.

Also Chi-Square test and F-test require that the original population be normally distributed.

Now for Testing a Claim about Variance or Standard Deviation

To test a claim about the value of the variance or the standard deviation of population, then we use the test statistic which follows chi-square distribution with n − 1 degrees of freedom, and is given by the following formula.

Where s is for given standard deviation and is for claimed standard deviation.

First we make Hypothesis, then we choose the value of α ( level of significance ), after that using above formula we find value of chi-square.

then we find table value for the chosen α also known as table value or p-value. Finally we give final answer by checking relation between p-value and α.

If  p-value < α then null hypothesis is rejected

If p-value > α  then null hypothesis accepted.