C D ng.cengage.com/static/nblui/index MIND TAP The t Test for Two Independent Sa
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C D ng.cengage.com/static/nblui/index MIND TAP The t Test for Two Independent Samples -Aplia a oue on Apr 1 at 5 AM CEST Aa Aa 7. Testing for homogeneity of variance A researcher wants to investigate claims that a new plant compound is effective in curbing appetite. She randomly assigns 26 rats to a treatment or control group (13 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 oonsumed by all 26 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 standard deviation (o) of the total caiories 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 775 with a standard deviation of 41, and the mean number of calories consumed by the rats in the control group is 984 with a standard deviation of 75. The researcher is unsure of which of the following required assumptions for the independent-measures t test? Are the observations within each group independent? Q Are the control and treatment groups independent of one another? Q Is there homogeneity of variance? Q Are the calories consumed by the rats in each group normally distributed?Explanation / Answer
1. Researcher is unsure of homogenity of variance. Hence,
c) Is there homogenity of variance.
2.
Fmax is calculated as the ratio of Larger variance to the smaller variance.
Here, we have larger Standard deviation = 75 and smaller Standard deviation = 41. Hence,
Fmax= 752/412 = 5625/1681 = 3.346.
Hence, Fmax = 3.346
3.
Critical value for Fmax statistics is given for given level of significance with k groups and n-1 degrees of freedom.
Here, level of significance = 0.05, Number of groups, k = 2 and Degrees of freedom , n - 1 = 13 -1 = 12
Hence, the F-max critical value for 0.05 level of significance for 2 groups with 12 degrees of freedom is given as 3.28.
4. Resercher's conclusion:
As the F-max calculted value of 3.346 is greater than the F-max ciritcal value of 3.28 the researches has to conclude that there is a significant difference in variance of groups, ie., Assumption of homogenity of variance is violated.
5.
Yes, you don't use a pooled variance and you recompute the degrees of freedom so that the resulting df is smaller.
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