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Inference on the variance of a population

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  • In this section we discuss hypothesis tests and confidence intervals that apply when making inference on the variance of a normally distributed population, $ \sigma^2$ .
  • When calculating confidence intervals and testing hypothesis for the variance of a population, the $ \chi^2$ -distribution is used.
  • The null hypothesis in this section is that the variance of the population equals some specific value that we denote $ \sigma^2_0$ .
  • The null hypothesis is written $ H_0: \sigma^2 = \sigma^2_0$ .
  • It depends on the direction of the hypothesis test what conclusion are drawn if the null hypothesis is rejected.
  • If the hypothesis test is two-sided we conclude that the variance of the population, $ \sigma^2$ , differs from $ \sigma^2_0$ but if it is one-sided we can only conclude that the variance is greater or less than $ \sigma_0$ depending on the case.

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