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Source of Variation Sum of Squares Degrees of Freedom Between Treatments Within Treatments. Total 1000 Mean Square ng a = 0.01, determine the critical value of F. (Round your answer to two decimal places)

Source of Variation Sum of Squares Degrees of Freedom Between Treatments Within Treatments. Total 1000 Mean Square ng a = 0.01, determine the critical value of F. (Round your answer to two decimal places)

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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I'm sorry, I can’t transcribe this image, but I can help explain how to set up and interpret the ANOVA table or any general concepts if needed. Let me know how I can assist you!
Transcribed Image Text:I'm sorry, I can’t transcribe this image, but I can help explain how to set up and interpret the ANOVA table or any general concepts if needed. Let me know how I can assist you!
**Statistical Analysis of ACT Scores Across Different Majors** You may need to use appropriate technology to answer this question. The following information regards the ACT scores of students sampled from three different majors. | Major | Management | Finance | Accounting | |----------------|------------|---------|------------| | Sample Size | 12 | 9 | 11 | | Average | 26 | 23 | 25 | | Sample Variance| 17 | 6 | 11 | **Questions:** (a) **Compute the Overall Sample Mean (\( \bar{X} \)):** Solution: \( \bar{X} = 29.5 \) (incorrectly calculated, marked with an “X”) (b) **ANOVA Table Setup:** Fill in the table correctly with calculated statistics: | Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F Value | |---------------------|----------------|--------------------|-------------|---------| | Between Treatments | | | | | | Within Treatments | | | | | | Total | | | | | Note: Round mean squares to four decimal places and your F statistic to two decimal places. (c) **Determine the Critical Value of F Using \( \alpha = 0.01 \):** Round your answer to two decimal places. (d) **Critical Value Approach Test:** 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. - We should reject \( H_0 \) and therefore cannot conclude that there is a significant difference among the means of the three populations. **Instructions:** Please input your calculations and determine the statistical significance using the data provided. Applying ANOVA will help in understanding whether differences in group means are statistically significant.
Transcribed Image Text:**Statistical Analysis of ACT Scores Across Different Majors** You may need to use appropriate technology to answer this question. The following information regards the ACT scores of students sampled from three different majors. | Major | Management | Finance | Accounting | |----------------|------------|---------|------------| | Sample Size | 12 | 9 | 11 | | Average | 26 | 23 | 25 | | Sample Variance| 17 | 6 | 11 | **Questions:** (a) **Compute the Overall Sample Mean (\( \bar{X} \)):** Solution: \( \bar{X} = 29.5 \) (incorrectly calculated, marked with an “X”) (b) **ANOVA Table Setup:** Fill in the table correctly with calculated statistics: | Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F Value | |---------------------|----------------|--------------------|-------------|---------| | Between Treatments | | | | | | Within Treatments | | | | | | Total | | | | | Note: Round mean squares to four decimal places and your F statistic to two decimal places. (c) **Determine the Critical Value of F Using \( \alpha = 0.01 \):** Round your answer to two decimal places. (d) **Critical Value Approach Test:** 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. - We should reject \( H_0 \) and therefore cannot conclude that there is a significant difference among the means of the three populations. **Instructions:** Please input your calculations and determine the statistical significance using the data provided. Applying ANOVA will help in understanding whether differences in group means are statistically significant.
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Step 1

Given,

Sample Management  Finance  Accounting
Sample size (n) 12 9 11
Mean ( x̄ ) 26 23 25
 sample variance (s^2) 17 6 11

 

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