e-Statistics

## Testing a Standard Deviation

Here we are interested in the plausibility of the statement regarding the population standard deviation  of a single variable. The null hypothesis  and the alternative hypothesis

forms a hypothesis test problem on whether we can reject  in favor of .''

The test procedure is based upon the sample standard deviation and the sample size . The normality assumption is essential for the appropriateness of the test. That is, sample size is adequately large (), or the sample distribution has a small sample size but is approximately normal. Then the test statistic is likely observed around, greater than, or less than the mean value of chi-square distribution under the respective null hypothesis  ,''  ,'' or  .'' The opposite of such observation is expressed by p-value < , suggesting an evidence against the null hypothesis .

When the null hypothesis is rejected it is reasonable to find out the confidence interval for the population standard deviation .

( , )