An executive at the home office of Big Rock Life Insurance is considering three branch managers as candidates for promotion to vice president. The branch reports include records showing sales volume for each salesperson in the branch (in hundreds of thousands of dollars). A random sample of these records was selected for salespersons in each branch. All three branches are located in cities in which per capita income is the same. The executive wishes to compare these samples to see if there is a significant difference in performance of salespersons in the three different branches. If so, the information will be used to determine which of the managers to promote. Branch Managed by Adams Branch Managed by McDale Branch Managed by Vasquez 7.8 8.2 6.7 6.6 10.7 8.9 10.5 11.5 10.9 10.6 9.2 11.2 9.7 10.8 Use a 1% level of significance. Shall we reject or not reject the claim that there are no differences among the performances of the salespersons in the different branches? (a) What is the level of significance? State the null and alternate hypotheses. Ho: μ1 = μ2 = μ3; H1: Not all the means are equal.Ho: μ1 = μ2 = μ3; H1: Exactly two means are equal. Ho: μ1 = μ2 = μ3; H1: At least two means are equal.Ho: μ1 = μ2 = μ3; H1: All three means are different. (b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Round your answers to three decimal places.) SSTOT = SSBET = SSW = Find d.f.BET, d.f.W, MSBET, and MSW. (Round your answers to three decimal places.) d.f.BET = d.f.W = MSBET = MSW = Find the value of the sample F statistic. (Round your answers to three decimal places.) What are the degrees of freedom? (numerator) (denominator) (c) Find the P-value of the sample test statistic. P-value > 0.1000.050 < P-value < 0.100 0.025 < P-value < 0.0500.010 < P-value < 0.0250.001 < P-value < 0.010P-value < 0.001 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Since the P value is greater than the level of significance at α = 0.01, we do not reject H0.Since the P value is less than or equal to the level of significance at α = 0.01, we reject H0. Since the P value is greater than the level of significance at α = 0.01, we reject H0.Since the P value is less than or equal to the level of significance at α = 0.01, we do not reject H0. (e) Interpret your conclusion in the context of the application. At the 1% level of significance there is insufficient evidence to conclude that the means are not all equal.At the 1% level of significance there is sufficient evidence to conclude that the means are all equal. At the 1% level of significance there is insufficient evidence to conclude that the means are all equal.At the 1% level of significance there is sufficient evidence to conclude that the means are not all equal. (f) Make a summary table for your ANOVA test. (Round your answers to three decimal places.) Source of Variation Sum of Squares Degrees of Freedom MS F Ratio P-Value Test Decision Between groups ---Select--- P-value > 0.100 0.050 < P-value < 0.100 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.001 < P-value < 0.010 P-value < 0.001 ---Select--- Do not reject H0. Reject H0. Within groups Total

An executive at the home office of Big Rock Life Insurance is considering three branch managers as candidates for promotion to vice president. The branch reports include records showing sales volume for each salesperson in the branch (in hundreds of thousands of dollars). A random sample of these records was selected for salespersons in each branch. All three branches are located in cities in which per capita income is the same. The executive wishes to compare these samples to see if there is a significant difference in performance of salespersons in the three different branches. If so, the information will be used to determine which of the managers to promote. Branch Managed by Adams Branch Managed by McDale Branch Managed by Vasquez 7.8 8.2 6.7 6.6 10.7 8.9 10.5 11.5 10.9 10.6 9.2 11.2 9.7 10.8 Use a 1% level of significance. Shall we reject or not reject the claim that there are no differences among the performances of the salespersons in the different branches? (a) What is the level of significance? State the null and alternate hypotheses. Ho: μ1 = μ2 = μ3; H1: Not all the means are equal.Ho: μ1 = μ2 = μ3; H1: Exactly two means are equal. Ho: μ1 = μ2 = μ3; H1: At least two means are equal.Ho: μ1 = μ2 = μ3; H1: All three means are different. (b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Round your answers to three decimal places.) SSTOT = SSBET = SSW = Find d.f.BET, d.f.W, MSBET, and MSW. (Round your answers to three decimal places.) d.f.BET = d.f.W = MSBET = MSW = Find the value of the sample F statistic. (Round your answers to three decimal places.) What are the degrees of freedom? (numerator) (denominator) (c) Find the P-value of the sample test statistic. P-value > 0.1000.050 < P-value < 0.100 0.025 < P-value < 0.0500.010 < P-value < 0.0250.001 < P-value < 0.010P-value < 0.001 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Since the P value is greater than the level of significance at α = 0.01, we do not reject H0.Since the P value is less than or equal to the level of significance at α = 0.01, we reject H0. Since the P value is greater than the level of significance at α = 0.01, we reject H0.Since the P value is less than or equal to the level of significance at α = 0.01, we do not reject H0. (e) Interpret your conclusion in the context of the application. At the 1% level of significance there is insufficient evidence to conclude that the means are not all equal.At the 1% level of significance there is sufficient evidence to conclude that the means are all equal. At the 1% level of significance there is insufficient evidence to conclude that the means are all equal.At the 1% level of significance there is sufficient evidence to conclude that the means are not all equal. (f) Make a summary table for your ANOVA test. (Round your answers to three decimal places.) Source of Variation Sum of Squares Degrees of Freedom MS F Ratio P-Value Test Decision Between groups ---Select--- P-value > 0.100 0.050 < P-value < 0.100 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.001 < P-value < 0.010 P-value < 0.001 ---Select--- Do not reject H0. Reject H0. Within groups Total

Name: An executive at the home office of Big Rock Life Insurance is consider
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: An executive at the home office of Big Rock Life Insurance is considering three branch managers as candidates for promotion to vice president. The branch reports include records showing sales volume for each salesperson in the branch (in hundreds of

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

Branch Managed by Adams	Branch Managed by McDale	Branch Managed by Vasquez
7.8	8.2	6.7
6.6	10.7	8.9
10.5	11.5	10.9
10.6	9.2	11.2
9.7
10.8

Use a 1% level of significance. Shall we reject or not reject the claim that there are no differences among the performances of the salespersons in the different branches?

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: μ₁ = μ₂ = μ₃; H₁: Not all the means are equal.H_o: μ₁ = μ₂ = μ₃; H₁: Exactly two means are equal. H_o: μ₁ = μ₂ = μ₃; H₁: At least two means are equal.H_o: μ₁ = μ₂ = μ₃; H₁: All three means are different.

(b) Find

SS_TOT, SS_BET, and SS_W

and check that

SS_TOT = SS_BET + SS_W.

(Round your answers to three decimal places.)

SS_TOT	=
SS_BET	=
SS_W	=

Find

d.f._BET, d.f._W, MS_BET, and MS_W.

(Round your answers to three decimal places.)

d.f._BET	=
d.f._W	=
MS_BET	=
MS_W	=

Find the value of the sample F statistic. (Round your answers to three decimal places.)

What are the degrees of freedom?
(numerator)
(denominator)

(c) Find the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100 0.025 < P-value < 0.0500.010 < P-value < 0.0250.001 < P-value < 0.010P-value < 0.001

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Since the P value is greater than the level of significance at α = 0.01, we do not reject H₀.Since the P value is less than or equal to the level of significance at α = 0.01, we reject H₀. Since the P value is greater than the level of significance at α = 0.01, we reject H₀.Since the P value is less than or equal to the level of significance at α = 0.01, we do not reject H₀.

(e) Interpret your conclusion in the context of the application.

At the 1% level of significance there is insufficient evidence to conclude that the means are not all equal.At the 1% level of significance there is sufficient evidence to conclude that the means are all equal. At the 1% level of significance there is insufficient evidence to conclude that the means are all equal.At the 1% level of significance there is sufficient evidence to conclude that the means are not all equal.

(f) Make a summary table for your ANOVA test. (Round your answers to three decimal places.)

Source of Variation	Sum of Squares	Degrees of Freedom	MS	F Ratio	P-Value	Test Decision
Between groups					---Select--- P-value > 0.100 0.050 < P-value < 0.100 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.001 < P-value < 0.010 P-value < 0.001	---Select--- Do not reject H0. Reject H0.
Within groups
Total

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step by step

Solved in 5 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Discrete Probability Distributions$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.