A researcher wants to investigate claims that a new plant compound is effective

Question

A researcher wants to investigate claims that a new plant compound is effective in curbing appetite. He randomly assigns 12 rats to treatment or control group (6 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 given a placebo. Over the course of the week, the researcher monitors the total number of calories consumed by all 12 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 placebo. Since the rats in the treatment group are independent of the rats in the control group, the researcher realizes that the design of his 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(sigma^2) 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 placebo. Suppose the mean number of weekly calories consumed by the rats given the plant compound (the treatment group) is 881 with a standard deviation of 76, and the mean number of calories consumed by the rats in the control group is 948 with a standard deviation of 60. 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? Are the observations within each group independent? Are the calories consumed by the rats in each group normally distributed? Is there homogeneity of variance? The researcher decides to use a Hartley's F max test. The value of F-mate is ___. Using the partial critical values for the F-max statistic table below, the critical value for the researchers F-max with alpha-.05 is ___. 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? 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 df is smaller. Yes, you don't use a pooled variance and you recompute the degrees of freedom so that the resulting df is larger

Explanation / Answer

Solution:

The Value of F-max is

F-max = s1^2/s2^2

F-max = (76)^2/(60)^2

F-max = 1.604

Since there are n = 12 (rats) and k =2 (number of treatments). The degrees of freedom would be n - 1 = 12 - 1 = 11.

From the table, the critical value is 3.72

Since F-max is less than the critical value, we fail to reject Ho.

Yes, you don't use a pooled variance and you recompute the degrees of freedom so that the resulting larger

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