Statement of a problem № m41170


Consider testing the hypothesis HA: σ21 > σ22 using samples of respective sizes 6 and 11. Note that we could represent this hypothesis as HA: σ21 > σ22 > 1. The samples yield s21 = 42.2 and s22 = 1.1. It hardly seems worth the time to conduct this test since the test statistic will obviously be very large, leading us to reject the null hypothesis. However, we might wish to test a hypothesis such as HA: σ21 > σ22 > 10. The test is conducted exactly the same way as the F -test of this chapter except that you use the test statistic F = (s21 / s22) (1 / k), where k = 10 for this hypothesis. Conduct the indicated test using a significance level of 0.05.

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