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The following null and alternative hypotheses need to be tested:
This corresponds to a two-tailed test, for which a F-test for two population variances needs to be used.
Based on the information provided, the significance level is degrees of freedom, and the the rejection region for this two-tailed test test is
The F-statistic is computed as follows:
Since from the sample information we get that
it is then concluded that the null hypothesis is not rejected.
Therefore, there is not enough evidence to claim that the population variance is different than the population variance at the significance level.