Link to us

If you think that our site could be of use to your website's visitors you can link to our site


Advertise Here

If you are interested in advertising on MathCracker.com, please follow the link below


     Chi-Square test for One Population Variance

Instructions: This calculator conducts a Chi-Square test for one population variance (\(\sigma^2\)). Please select the null and alternative hypotheses, type the hypothesized variance, the significance level, the sample variance, and the sample size, and the results of the Chi-Square test will be presented for you:


Ho: \(\sigma^2\)     \(\sigma_0^2\)

Ha: \(\sigma^2\)      \(\sigma_0^2\)

Hypothesized Variance (\(\sigma_0^2\)) =   

Sample Variance (\(s^2\)) =   

Sample Size (n) =

Significance Level (\(\alpha\)) = (Ex: 0.01, 0.05, or 5, 10 without "%", etc)





More about the Chi-Square test for one variance so you can better understand the results provided by this solver: A Chi-Square test for one population variance is a hypothesis that attempts to make a claim about the population variance (\(\sigma^2\)) based on sample information.

The test, as every other well formed hypothesis test, has two non-overlaping hypotheses, the null and the alternative hypothesis. The null hypothesis is a statement about the population variance which represents the assumption of no effect, and the alternative hypothesis is the complementary hypothesis to the null hypothesis. The main properties of a one sample Chi-Square test for one population variance are:

  • The distribution of the test statistic is the Chi-Square distribution, with n-1 degrees of freedom

  • The Chi-Square distribution is one of the most important distributions in statistics, together with the normal distribution and the F-distribution

  • Depending on our knowledge about the "no effect" situation, the Chi-Square test can be two-tailed, left-tailed or right-tailed

  • The main principle of hypothesis testing is that the null hypothesis is rejected if the test statistic obtained is sufficiently unlikely under the assumption that the null hypothesis is true

  • The p-value is the probability of obtaining sample results as extreme or more extreme than the sample results obtained, under the assumption that the null hypothesis is true

  • In a hypothesis tests there are two types of errors. Type I error occurs when we reject a true null hypothesis, and the Type II error occurs when we fail to reject a false null hypothesis

The formula for a Chi-Square statistic is

\[\chi^2 = \frac{(n-1)s^2}{\sigma^2}\]

The null hypothesis is rejected when the Chi-Square statistic lies on the rejection region, which is determined by the significance level (\(\alpha\)) and the type of tail (two-tailed, left-tailed or right-tailed).



Get solved Math Problems, Math Cracks, Tips and Tutorials delivered weekly to your inbox

* indicates required




In case you have any suggestion, please do not hesitate to contact us.