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Consider dot plots 1 and 2 shown below. Assume that the

Statistics for Business and Economics | 12th Edition | ISBN: 9780321826237 | Authors: James T. McClave, P. George Benson, Terry T Sincich ISBN: 9780321826237 51

Solution for problem 17E Chapter 9

Statistics for Business and Economics | 12th Edition

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Statistics for Business and Economics | 12th Edition | ISBN: 9780321826237 | Authors: James T. McClave, P. George Benson, Terry T Sincich

Statistics for Business and Economics | 12th Edition

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Problem 17E

Problem 17E

Consider dot plots 1 and 2 shown below. Assume that the two samples represent independent, random samples corresponding to two treatments in a completely randomized design.

a. In which plot is the difference between the sample means small relative to the variability within the sample observations? Justify your answer.

b. Calculate the treatment means (i.e., the means of samples 1 and 2) for both dot plots.

c. Use the means to calculate the Sum of Squares for Treatments (SST) for each dot plot.

d. Calculate the sample variance for each sample and use these values to obtain the Sum of Squares for Error (SSE) for each dot plot.

e. Calculate the Total Sum of Squares [SS(Total)] for the two dot plots by adding the Sums of Squares for Treatments and Error. What percentage of SS(Total) is accounted for by the treatments—that is, what percentage of the Total Sum of Squares is the Sum of Squares for Treatments—in each case?

f. Convert the Sums of Squares for Treatments and Error to mean squares by dividing each by the appropriate number of degrees of freedom. Calculate the F-ratio of the Mean Square for Treatments (MST) to the Mean Square for Error (MSE) for each dot plot.

g. Use the F-ratios to test the null hypothesis that the two samples are drawn from populations with equal means. Use α = .05.

h. What assumptions must be made about the probability distributions corresponding to the responses for each treatment to ensure the validity of the F-tests conducted in part g?

Step-by-Step Solution:

Problem 17E

Consider dot plots 1 and 2 shown below. Assume that the two samples represent independent, random samples corresponding to two treatments in a completely randomized design.

a. In which plot is the difference between the sample means small relative to the variability within the sample observations? Justify your answer.

b. Calculate the treatment means (i.e., the means of samples 1 and 2) for both dot plots.

c. Use the means to calculate the Sum of Squares for Treatments (SST) for each dot plot.

d. Calculate the sample variance for each sample and use these values to obtain the Sum of Squares for Error (SSE) for each dot plot.

e. Calculate the Total Sum of Squares [SS(Total)] for the two dot plots by adding the Sums of Squares for Treatments and Error. What percentage of SS(Total) is accounted for by the treatments—that is, what percentage of the Total Sum of Squares is the Sum of Squares for Treatments—in each case?

f. Convert the Sums of Squares for Treatments and Error to mean squares by dividing each by the appropriate number of degrees of freedom. Calculate the F-ratio of the Mean Square for Treatments (MST) to the Mean Square for Error (MSE) for each dot plot.

g. Use the F-ratios to test the null hypothesis that the two samples are drawn from populations with equal means. Use ? = .05.

h. What assumptions must be made about the probability distributions corresponding to the responses for each treatment to ensure the validity of the F-tests conducted in part g?

                                                       Step-by-step solution

Step 1 of 10

a)  Plot#2 is the difference between the sample means small relative to the variability within the sample observations. Because if the samples are depicted in the dot plot,  then the difference between the means is small relative to the sampling variability of the samples within the treatments-Two samples. We would be inclined not to reject the null hypothesis of equal population means.

Step 2 of 10

Chapter 9, Problem 17E is Solved
Step 3 of 10

Textbook: Statistics for Business and Economics
Edition: 12
Author: James T. McClave, P. George Benson, Terry T Sincich
ISBN: 9780321826237

This full solution covers the following key subjects: squares, treatments, Dot, sum, means. This expansive textbook survival guide covers 15 chapters, and 1631 solutions. Since the solution to 17E from 9 chapter was answered, more than 396 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Statistics for Business and Economics , edition: 12. The full step-by-step solution to problem: 17E from chapter: 9 was answered by , our top Business solution expert on 07/21/17, 05:42AM. The answer to “Consider dot plots 1 and 2 shown below. Assume that the two samples represent independent, random samples corresponding to two treatments in a completely randomized design.a. In which plot is the difference between the sample means small relative to the variability within the sample observations? Justify your answer.b. Calculate the treatment means (i.e., the means of samples 1 and 2) for both dot plots.c. Use the means to calculate the Sum of Squares for Treatments (SST) for each dot plot.d. Calculate the sample variance for each sample and use these values to obtain the Sum of Squares for Error (SSE) for each dot plot.e. Calculate the Total Sum of Squares [SS(Total)] for the two dot plots by adding the Sums of Squares for Treatments and Error. What percentage of SS(Total) is accounted for by the treatments—that is, what percentage of the Total Sum of Squares is the Sum of Squares for Treatments—in each case?f. Convert the Sums of Squares for Treatments and Error to mean squares by dividing each by the appropriate number of degrees of freedom. Calculate the F-ratio of the Mean Square for Treatments (MST) to the Mean Square for Error (MSE) for each dot plot.g. Use the F-ratios to test the null hypothesis that the two samples are drawn from populations with equal means. Use ? = .05.h. What assumptions must be made about the probability distributions corresponding to the responses for each treatment to ensure the validity of the F-tests conducted in part g?” is broken down into a number of easy to follow steps, and 248 words. Statistics for Business and Economics was written by and is associated to the ISBN: 9780321826237.

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