clude that the population van Aces are not equal. The hypothesis tesis of equality of van ances are summarized as follows Tests of Equality of Variances from Two Normal Populations Lets and be observed sample variances from independent random samples of size n, and n, from normally distributed populations with variances and er. Use s to denote the larger variance. Then the following tests have significance level a: 1. To test either null hypothesis H: - , are Hp-rs against the alternative 110.191 the decision rule is as follows: Troject HUFF 2. To test the null hypothesis He- against the two-sided alternative the decision rule is as follows: met H, IF-> 110 201 where s is the larger of the two sample variances. Since either sample variance could be larger, this rule is actually based on a two-tailed test, and hence, we use a/2 as the upper-tail probability Here, Fin the number for which PE->) - where Fichas an F distribution with t, - 1) numerator degrees of freedom and (, - 1) denominator degrees of freedom. Hypothee Testing Additional Topics u6 For all these tests a p-value is the probability of getting a value at least as extreme as the one obtained, given the null hypothesis. Because of the com- plexity of the F distribution, critical values are computed for only a few special cases. Thus, p-values will be typically computed using a statistical package such as Minitab. Example 10.6 Study of Maturity Variances (Hypothesis Tests for the Equality of Two Variances) The research staff of Investors Now, an online financial trading firm, was interested in determining if there is a difference in the variance of the maturities of AAA-rated in- dustrial bonds compared to CCC-rated industrial bonds