12. Testing for homogeneity of variance A researcher wants to investigate claims that a new plant compound is effective in curbing appetite. She randomly assigns 32 rats to a treatment or control group (16 rats in each group). Rats in the treatment group are given the plant compound daily for a week, while rats in the control group are A-Z given a placebo. Over the course of the week, the researcher monitors the total number of calories consumed by all 32 rats. All the rats are kept separate from one another, but in their typical environments, for the duration of the week. The researcher's null hypothesis is that the rats given the plant compound consume the same number of calories as the rats given a placebo. Since the rats in the treatment group are independent of the rats in the control group, the researcher realizes that the design of her study is an independent-measures design. The researcher knows that the total calories consumed by a rat over the course of a week are normally distributed. However, the researcher is not sure that the variance (0?) of the total calories consumed by a rat over the course of a week is the same regardless of whether the rat is given the plant compound or a placebo. Suppose the mean number of weekly calories consumed by the rats given the plant compound (the treatment group) is 839 with a standard deviation of 42, and the mean number of calories consumed by the rats in the control group is 881 with a standard deviation of 90. The researcher is unsure of which of the following required assumptions for the independent-measures t test? Are the control and treatment groups independent of one another? O Is there homogeneity of variance? O Are the observations within each group independent? Are the calories consumed by the rats in each group normally distributed? O The researcher decides to use a Hartley's F-max test. The value of F-max is Using the partial Critical Values for the F-max Statistic table below, the critical value for the researcher's F-max with a = 0.05 is Critical Values for the F-max Statistic (Partial)Problem Set: Chapter 10 The t Test for Two Independent Samples X Critical values for a = .05 are in regular type; critical values for a = .01 are bold. k = Number of Samples n- 1 2 3 A-Z 9.60 15.5 23.2 37.0 5 7.15 10.8 14.9 22.0 5.82 8.38 11.1 15.5 7 4.99 6.94 8.89 12.1 CO 4.43 6.00 7.50 9.9 9 4.03 5.34 6.54 8.5 10 3.72 4.85 5.85 7.4 12 3.28 4.16 4.91 6.1 O 15 2.86 3.54 4.07 4.9 20 2.46 2.95 3.32 3.8 30 2.07 2.40 2.63 3.0Problem Set: Chapter 10 The t Test for Two Independent Samples X 10 3.72 4.85 5.85 7.4 12 3.28 4.16 4.91 6.1 A-Z 15 2.86 3.54 4.07 4.9 20 2.46 2.95 3.32 3.8 30 2.07 2.40 2.63 3.0 60 1.67 1.85 1.96 2.2 Given the results of the F-max test, the researcher's conclusion is that Can you still use the independent-measures t test if the homogeneity of variance assumption is violated? Yes, you don't use a pooled variance and you recompute the degrees of freedom so that the resulting of is smaller. No, you cannot use the independent-measures t test. Yes, you don't use a pooled variance and you recompute the degrees of freedom so that the resulting of is larger. Grade It Now Save & Continue Continue without saving