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Test Statistic for Hypothesis Tests Concerning Value of Population Variance (Normally Distributed Population)
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\(\chi^{2} = \frac{(n-1)\times s^{2}}{\sigma^{2}_{0}}\)

  • \(\chi^{2}\) - chi-square statistic with n-1 degrees of freedom
  • \(n\) - number of independent observations
  • \(s^{2}\) - sample variance
  • \(\sigma^{2}_{0}\) - value of the population variance under null hypothesis

A chi-square distribution is defined by one parameter (the number of degrees of freedom), is asymmetrical, and is bounded below by zero.

Values of the chi-square test are usually given in the table for probability in the right tail.

\(\alpha\) probability in the right tail = \((1-\alpha)\) probability in the left tail

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