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A researcher wants to investigate claims that a new plant compound is effective in curbing appetite. He 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 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 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?

Are the control and treatment groups independent of one another?

Are the observations within each group independent?

Is there homogeneity of variance?

Are the calories consumed by the rats in each group normally distributed?

Respuesta :

Answer:

Correct option: Is there homogeneity of variance?

Step-by-step explanation:

An independent sample t-test is used to determine whether there is a significant difference between the two population means.

The hypothesis can be defined as:

H₀: There is no difference between the two means, i.e. μ₁ = μ₂.

Hₐ: There is a significant difference between the two means, i.e. μ₁ ≠ μ₂.

The assumptions of t-test are:

  1. The samples are drawn from two independent populations.
  2. The population distribution of the two populations must be normally distributed.
  3. The variances of the two population must be equal, or there should be homogeneity of the variances.

Thus, the researcher is unsure of whether there is homogeneity of variance or not.

Thus, the correct option is: Is there homogeneity of variance?

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