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You may need to use the appropriate technology to answer this question. Information regarding the ACT scores of samples of students in three different majors is given below. Sample Size Average Management Within Treatments 12 Sample Variance (a) Compute the overall sample mean. 29.5 x Total 26 17 Major Finance 9 23 6 Accounting 11 25. (b) Set up the ANOVA table for this problem including the test statistic. (Round your mean squares to four decimal places and your F statistic to two decimal places.) Source of Variation Sum of Squares Degrees of Freedom Mean Square Between Treatments 11 (c) Using a = 0.01, determine the critical value of F. (Round your answer to two decimal places.) F

You may need to use the appropriate technology to answer this question. Information regarding the ACT scores of samples of students in three different majors is given below. Sample Size Average Management Within Treatments 12 Sample Variance (a) Compute the overall sample mean. 29.5 x Total 26 17 Major Finance 9 23 6 Accounting 11 25. (b) Set up the ANOVA table for this problem including the test statistic. (Round your mean squares to four decimal places and your F statistic to two decimal places.) Source of Variation Sum of Squares Degrees of Freedom Mean Square Between Treatments 11 (c) Using a = 0.01, determine the critical value of F. (Round your answer to two decimal places.) F

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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You may need to use the appropriate technology to answer this question. Information regarding the ACT scores of samples of students in three different majors is given below: | Major | Management | Finance | Accounting | |-----------------|------------|---------|------------| | Sample Size | 12 | 9 | 11 | | Average | 26 | 23 | 25 | | Sample Variance | 17 | 6 | 11 | (a) Compute the overall sample mean \(\bar{X}\). \[ \bar{X} = 29.5 \] (b) Set up the ANOVA table for this problem including the test statistic. (Round your mean squares to four decimal places and your \( F \) statistic to two decimal places.) | Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | |---------------------|----------------|--------------------|-------------|-------| | Between Treatments | | | | | | Within Treatments | | | | | | Total | | | | | (c) Using \(\alpha = 0.01\), determine the critical value of \( F \). (Round your answer to two decimal places.) (d) Using the critical value approach, test to determine whether there is a significant difference in the means of the three populations. - We should not reject \( H_0 \) and therefore can conclude that there is a significant difference among the means of the three populations. - We should not reject \( H_0 \) and therefore cannot conclude that there is a significant difference among the means of the three populations. - We should reject \( H_0 \) and therefore can conclude that there is a significant difference among the means of the three populations. **Note:** Since the fields for calculations (such as sum of squares, degrees of freedom, mean square, and F values) are blank, further computation is needed to complete the ANOVA table.
Transcribed Image Text:You may need to use the appropriate technology to answer this question. Information regarding the ACT scores of samples of students in three different majors is given below: | Major | Management | Finance | Accounting | |-----------------|------------|---------|------------| | Sample Size | 12 | 9 | 11 | | Average | 26 | 23 | 25 | | Sample Variance | 17 | 6 | 11 | (a) Compute the overall sample mean \(\bar{X}\). \[ \bar{X} = 29.5 \] (b) Set up the ANOVA table for this problem including the test statistic. (Round your mean squares to four decimal places and your \( F \) statistic to two decimal places.) | Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | |---------------------|----------------|--------------------|-------------|-------| | Between Treatments | | | | | | Within Treatments | | | | | | Total | | | | | (c) Using \(\alpha = 0.01\), determine the critical value of \( F \). (Round your answer to two decimal places.) (d) Using the critical value approach, test to determine whether there is a significant difference in the means of the three populations. - We should not reject \( H_0 \) and therefore can conclude that there is a significant difference among the means of the three populations. - We should not reject \( H_0 \) and therefore cannot conclude that there is a significant difference among the means of the three populations. - We should reject \( H_0 \) and therefore can conclude that there is a significant difference among the means of the three populations. **Note:** Since the fields for calculations (such as sum of squares, degrees of freedom, mean square, and F values) are blank, further computation is needed to complete the ANOVA table.
### Educational Content on ANOVA Analysis #### ANOVA Problem Breakdown **(a) Compute the Overall Sample Mean \(\bar{X}\):** The calculated overall sample mean is **29.5**. This calculation was marked incorrect as indicated by the red "X". --- **(b) Set up the ANOVA Table:** The table is designed to organize the ANOVA results, including the test statistic. Inputs should be rounded to four decimal places for mean squares and two decimal places for the F statistic. - **Source of Variation:** - Between Treatments - Within Treatments - Total - **Table Columns:** - Sum of Squares - Degrees of Freedom - Mean Square - F (Statistic) Entries for these columns need to be filled in based on the specific problem details. --- **(c) Determine the Critical Value of F (with \(\alpha = 0.01\)):** Round your answer to two decimal places to find the critical value. --- **(d) Using the Critical Value Approach:** Determine if there is a significant difference in the means of the three populations. - Options: - We should not reject \(H_0\) and therefore cannot conclude that there is a significant difference among the means of the three populations. - We should not reject \(H_0\) and therefore can conclude that there is a significant difference among the means of the three populations. - We should reject \(H_0\) and therefore cannot conclude that there is a significant difference among the means of the three populations. - We should reject \(H_0\) and therefore can conclude that there is a significant difference among the means of the three populations. The correct choice is marked: - **We should reject \(H_0\) and therefore can conclude that there is a significant difference among the means of the three populations.** --- **(e) Determine the p-value and Use it for the Test:** Round your answer to three decimal places. - **The p-value __:** Since this is greater than the significance level, we **should not** reject \(H_0\) and conclude that there is not sufficient evidence in the data to suggest a significant difference among the mean ACT scores of the three majors. --- **Help Section:** For additional guidance, a "Need Help?" option with a link to "Read It" is available. ####
Transcribed Image Text:### Educational Content on ANOVA Analysis #### ANOVA Problem Breakdown **(a) Compute the Overall Sample Mean \(\bar{X}\):** The calculated overall sample mean is **29.5**. This calculation was marked incorrect as indicated by the red "X". --- **(b) Set up the ANOVA Table:** The table is designed to organize the ANOVA results, including the test statistic. Inputs should be rounded to four decimal places for mean squares and two decimal places for the F statistic. - **Source of Variation:** - Between Treatments - Within Treatments - Total - **Table Columns:** - Sum of Squares - Degrees of Freedom - Mean Square - F (Statistic) Entries for these columns need to be filled in based on the specific problem details. --- **(c) Determine the Critical Value of F (with \(\alpha = 0.01\)):** Round your answer to two decimal places to find the critical value. --- **(d) Using the Critical Value Approach:** Determine if there is a significant difference in the means of the three populations. - Options: - We should not reject \(H_0\) and therefore cannot conclude that there is a significant difference among the means of the three populations. - We should not reject \(H_0\) and therefore can conclude that there is a significant difference among the means of the three populations. - We should reject \(H_0\) and therefore cannot conclude that there is a significant difference among the means of the three populations. - We should reject \(H_0\) and therefore can conclude that there is a significant difference among the means of the three populations. The correct choice is marked: - **We should reject \(H_0\) and therefore can conclude that there is a significant difference among the means of the three populations.** --- **(e) Determine the p-value and Use it for the Test:** Round your answer to three decimal places. - **The p-value __:** Since this is greater than the significance level, we **should not** reject \(H_0\) and conclude that there is not sufficient evidence in the data to suggest a significant difference among the mean ACT scores of the three majors. --- **Help Section:** For additional guidance, a "Need Help?" option with a link to "Read It" is available. ####
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