Attempts: Average: /5 12. Testing for homogeneity of variance Aa Aa A researcher

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Attempts: Average: /5 12. Testing for homogeneity of variance Aa Aa A researcher wants to investigate claims that a new plant compound is effective in curbing appetite. She randomly assigns 18 rats to a treatment or control group (9 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 18 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 (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 a placebo Suppose the mean number of weekly calories consumed by the rats given the plant compound (the treatment group) is 634 with a standard deviation of 39, and the mean number of calories consumed by the rats in the control group is 790 with a standard deviation of 87 The researcher is unsure of which of the following required assumptions for the independent-measures t test? O Are the calories consumed by the rats in each group normally distributed? O Are the control and treatment groups independent of one another? O Is there homogeneity of variance? O Are the observations within each group independent? 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 = .01 is Critical Values for the F-max Statistic (Partial) Critical values for = .05 are in regular type; critical values for = .01 are bold

Explanation / Answer

Answer 1 : The required assumption is " Is there homogenity of variance"?

Answer 2 : Here F - max as (n-1) = 8 and alpha = 0.01 , F(max) = 7.50

Here value of F = larger of variance/smaller variance = 872 /392 = 4.976

So here F < F - max

so we can conclude that there is homogenity of variance at the significance level alpha = 0.01 and dF = 8

QUestion 3. If homogenity of variance assumption is violated, we can still use independent meansure t - test as we dont use a pooled variance and we can recompute the degrees of freedom so that the resulting df is smaller. Option b is correct. This test will be called independent -measure t test for unequal variances.

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