How productive are U.S. workers? One way to answer this question is to study annual profits per employee. A random sample of companies in computers (I), aerospace (II), heavy equipment (III), and broadcasting (IV) gave the following data regarding annual profits per employee (units in thousands of dollars). I II III IV 27.9 13.2 22.5 17.5 23.1 9.6 20.4 16.5 14.6 11.6 7.5 14.2 8.3 8.5 12.1 15.7 11.4 6.4 7.6 10.5 19.4 9.8 Shall we reject or not reject the claim that there is no difference in population mean annual profits per employee in each of the four types of companies? Use a 5% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. Ho: ?1 = ?2 = ?3 = ?4; H1: Exactly three means are equal.Ho: ?1 = ?2 = ?3 = ?4; H1: All four means are different. Ho: ?1 = ?2 = ?3 = ?4; H1: Exactly two means are equal.Ho: ?1 = ?2 = ?3 = ?4; H1: Not all the means are equal. (b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.) SSTOT = SSBET = SSW = Find d.f.BET, d.f.W, MSBET, and MSW. (Use 3 decimal places for MSBET, and MSW.) dfBET = dfW = MSBET = MSW = Find the value of the sample F statistic. (Use 3 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 ? = 0.05, we do not reject H0.Since the P-value is less than or equal to the level of significance at ? = 0.05, we reject H0. Since the P-value is greater than the level of significance at ? = 0.05, we reject H0.Since the P-value is less than or equal to the level of significance at ? = 0.05, we do not reject H0. (e) Interpret your conclusion in the context of the application. At the 5% level of significance there is insufficient evidence to conclude that the means are not all equal.At the 5% level of significance there is sufficient evidence to conclude that the means are all equal. At the 5% level of significance there is insufficient evidence to conclude that the means are all equal.At the 5% 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. 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
How productive are U.S. workers? One way to answer this question is to study annual profits per employee. A random sample of companies in computers (I), aerospace (II), heavy equipment (III), and broadcasting (IV) gave the following data regarding annual profits per employee (units in thousands of dollars). I II III IV 27.9 13.2 22.5 17.5 23.1 9.6 20.4 16.5 14.6 11.6 7.5 14.2 8.3 8.5 12.1 15.7 11.4 6.4 7.6 10.5 19.4 9.8 Shall we reject or not reject the claim that there is no difference in population mean annual profits per employee in each of the four types of companies? Use a 5% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. Ho: ?1 = ?2 = ?3 = ?4; H1: Exactly three means are equal.Ho: ?1 = ?2 = ?3 = ?4; H1: All four means are different. Ho: ?1 = ?2 = ?3 = ?4; H1: Exactly two means are equal.Ho: ?1 = ?2 = ?3 = ?4; H1: Not all the means are equal. (b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.) SSTOT = SSBET = SSW = Find d.f.BET, d.f.W, MSBET, and MSW. (Use 3 decimal places for MSBET, and MSW.) dfBET = dfW = MSBET = MSW = Find the value of the sample F statistic. (Use 3 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 ? = 0.05, we do not reject H0.Since the P-value is less than or equal to the level of significance at ? = 0.05, we reject H0. Since the P-value is greater than the level of significance at ? = 0.05, we reject H0.Since the P-value is less than or equal to the level of significance at ? = 0.05, we do not reject H0. (e) Interpret your conclusion in the context of the application. At the 5% level of significance there is insufficient evidence to conclude that the means are not all equal.At the 5% level of significance there is sufficient evidence to conclude that the means are all equal. At the 5% level of significance there is insufficient evidence to conclude that the means are all equal.At the 5% 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. 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
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter5: A Survey Of Other Common Functions
Section5.3: Modeling Data With Power Functions
Problem 6E: Urban Travel Times Population of cities and driving times are related, as shown in the accompanying...
Related questions
Topic Video
Question
How productive are U.S. workers? One way to answer this question is to study annual profits per employee. A random sample of companies in computers (I), aerospace (II), heavy equipment (III), and broadcasting (IV) gave the following data regarding annual profits per employee (units in thousands of dollars).
I | II | III | IV |
27.9 | 13.2 | 22.5 | 17.5 |
23.1 | 9.6 | 20.4 | 16.5 |
14.6 | 11.6 | 7.5 | 14.2 |
8.3 | 8.5 | 12.1 | 15.7 |
11.4 | 6.4 | 7.6 | 10.5 |
19.4 | 9.8 |
Shall we reject or not reject the claim that there is no difference in population mean annual profits per employee in each of the four types of companies? Use a 5% level of significance.
(a) What is the level of significance?
State the null and alternate hypotheses.
(b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.)
Find d.f.BET, d.f.W, MSBET, and MSW. (Use 3 decimal places for MSBET, and MSW.)
Find the value of the sample F statistic. (Use 3 decimal places.)
What are the degrees of freedom?
(numerator)
(denominator)
(c) Find the P-value of the sample test statistic.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?
(e) Interpret your conclusion in the context of the application.
(f) Make a summary table for your ANOVA test.
State the null and alternate hypotheses.
Ho: ?1 = ?2 = ?3 = ?4; H1: Exactly three means are equal.Ho: ?1 = ?2 = ?3 = ?4; H1: All four means are different. Ho: ?1 = ?2 = ?3 = ?4; H1: Exactly two means are equal.Ho: ?1 = ?2 = ?3 = ?4; H1: Not all the means are equal.
(b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.)
SSTOT | = | |
SSBET | = | |
SSW | = |
Find d.f.BET, d.f.W, MSBET, and MSW. (Use 3 decimal places for MSBET, and MSW.)
dfBET | = | |
dfW | = | |
MSBET | = | |
MSW | = |
Find the value of the sample F statistic. (Use 3 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 ? = 0.05, we do not reject H0.Since the P-value is less than or equal to the level of significance at ? = 0.05, we reject H0. Since the P-value is greater than the level of significance at ? = 0.05, we reject H0.Since the P-value is less than or equal to the level of significance at ? = 0.05, we do not reject H0.
(e) Interpret your conclusion in the context of the application.
At the 5% level of significance there is insufficient evidence to conclude that the means are not all equal.At the 5% level of significance there is sufficient evidence to conclude that the means are all equal. At the 5% level of significance there is insufficient evidence to conclude that the means are all equal.At the 5% 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.
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 |
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 1 images
Knowledge Booster
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.Recommended textbooks for you
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill