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Inference on the variance of two populations

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  • The hypothesis tests that we discuss in this section are used to compare the variance of two populations that both are normally distributed.
  • Tests of this kind are often conducted before hypothesis tests where the means of two populations are compared and the variance of the populations is unknown and the samples are not large.
  • The null hypothesis i this section is that the variance of the two populations is equal, written $ H_0: \sigma_1^2 = \sigma_2^2$ .
  • If the hypothesis test is two-sided we can draw the conclusion that the variances are unequal, but if it is one-sided we can only draw the conclusion that the variance in one sample is greater then the variance in the other sample.





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