A researcher wants to investigate claims that a new plant compound is effective in curbing appetite. She randomly assigns 22 rats to a treatment or control group (11 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 22 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 (σ²) 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 843 with a standard deviation of 111, and the mean number of calories consumed by the rats in the control group is 946 with a standard deviation of 73. The researcher is unsure of which of the following required assumptions for the independent-measures t test? Are the observations within each group independent? Is there homogeneity of variance? Are the calories consumed by the rats in each group normally distributed? Are the control and treatment groups independent of one another? 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 α = 0.01 is . Critical Values for the F-max Statistic (Partial) Critical values for α = .05 are in regular type; critical values for α = .01 are bold. k = Number of Samples n – 1 2 3 4 9.60 15.5 23.2 37.0 5 7.15 10.8 14.9 22.0 6 5.82 8.38 11.1 15.5 7 4.99 6.94 8.89 12.1 8 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 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 df is larger. 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.

A researcher wants to investigate claims that a new plant compound is effective in curbing appetite. She randomly assigns 22 rats to a treatment or control group (11 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 22 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 (σ²) 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 843 with a standard deviation of 111, and the mean number of calories consumed by the rats in the control group is 946 with a standard deviation of 73. The researcher is unsure of which of the following required assumptions for the independent-measures t test? Are the observations within each group independent? Is there homogeneity of variance? Are the calories consumed by the rats in each group normally distributed? Are the control and treatment groups independent of one another? 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 α = 0.01 is . Critical Values for the F-max Statistic (Partial) Critical values for α = .05 are in regular type; critical values for α = .01 are bold. k = Number of Samples n – 1 2 3 4 9.60 15.5 23.2 37.0 5 7.15 10.8 14.9 22.0 6 5.82 8.38 11.1 15.5 7 4.99 6.94 8.89 12.1 8 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 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 df is larger. 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.

Name: A researcher wants to investigate claims that a new plant compound is
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Description: A researcher wants to investigate claims that a new plant compound is effective in curbing appetite. She randomly assigns 22 rats to a treatment or control group (11 rats in each group). Rats in the treatment group are given the plant compound daily

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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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 (σ²) 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 843 with a standard deviation of 111, and the mean number of calories consumed by the rats in the control group is 946 with a standard deviation of 73.

The researcher is unsure of which of the following required assumptions for the independent-measures t test?

Are the observations within each group independent?

Is there homogeneity of variance?

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

Are the control and treatment groups independent of one another?

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 α = 0.01 is .

Critical Values for the F-max Statistic (Partial)

Critical values for α = .05 are in regular type; critical values for α = .01 are bold.

k = Number of Samples
n – 1	2	3
4	9.60	15.5
	23.2	37.0
5	7.15	10.8
	14.9	22.0
6	5.82	8.38
	11.1	15.5
7	4.99	6.94
	8.89	12.1
8	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
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 df is larger.

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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1

Given:

${\bar{x}}_{1} = 843 s_{1} = 111 {\bar{x}}_{2} = 946 s_{2} = 73 n_{1} = n_{2} = 11 α = 0.01$

The required assumptions for the independent-measures t test is, Is there homogeneity of variance?

The test hypothesis are,

H₀: σ₁² = σ₂²

H₁: σ₁² ≠ σ₂²

This is a two-tailed test.

We reject the null hypothesis if F-value > F-critical value.

The critical value for the researcher’s F-max with α = 0.01 is 5.85.

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