Question

A random sample of size ny = 36 yields a variance of 6.2, and a random sample of size n2 = 37 yields a variance of 8.4. At a = 0.01, test the claim that the variance of Population 1 is less than the variance of Population 2. 1. The alternate hypothesis is Ha: si < 82 Οσι < σ2 oo <o Osi <s 2. This is a left tailed test with: dfn- and dfa - 3a. The STS (to 2 decimals) is F= 3b. The P-value (to 3 decimals) is: 4a. At a = 0.01, the decision is: O Reject Ho O Accept Ho O Accept Ha O Do not reject Ho 4b. The conclusion is: O There is insufficient evidence to support the claim that o is less than a There is sufficient evidence to support the claim that is less than o O There is insufficient evidence to reject the claim that o is less than oz There is sufficient evidence to reject the claim that o is less than o Submit Question

Answer 1

Solution: The provided sample variances are si = 6.2 and sź = 8.4 and the sample sizes are given by n1 = 36 and ng = 37. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: a = of Ha:of < This corresponds to a left-tailed test, for which a F-test for two population variances needs to be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.01, and the the rejection region for this left-tailed test is R = {F:F<Fi = 0.45). (3) Test Statistics The F-statistic is computed as follows: F = 6.2 8.4 0.738 15701 (4) Decision about the null hypothesis Since from the sample information we get that F = 0.738 > F1 = 0.45, it is then concluded that the null hypothesis is not rejected. (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population variance o is less than the population variance oš, at the a = 0.01 significance level.