**Educational Website: ACT Scores Analysis Using ANOVA**The table below presents information regarding ACT scores of samples of students in three different majors. This data is crucial for conducting an ANOVA (Analysis of Variance) to compare the groups.| **Major** | **Management** | **Finance** | **Accounting** ||-------------------|----------------|-------------|----------------|| **Sample Size** | 12 | 9 | 11 || **Average** | 26 | 23 | 25 || **Sample Variance** | 17 | 29 | 11 |**Tasks:**(a) **Compute the overall sample mean (\(\overline{X}\)):**- The initial computation in the image shows a mean of 29.5, but it is marked incorrect, indicating a need for re-evaluation.(b) **Set up the ANOVA table for this problem:**- Include calculations for Sum of Squares, Degrees of Freedom, Mean Square, and the F statistic. Ensure to round your numbers to four decimal places.| **Source of Variation** | **Sum of Squares** | **Degrees of Freedom** | **Mean Square** | **F** ||-------------------------|--------------------|------------------------|----------------|-------|| Between Treatments | | | | || Within Treatments | | | | || **Total** | | | | |(c) **Critical Value of \( F \):**- Using \( \alpha = 0.01 \), determine the critical value of \( F \). Round your answer to two decimal places.(d) **Conclusion Using the Critical Value Approach:**Test to determine if there is a significant difference in the means of the three populations.- **Options:** - We should not reject \( H_0 \) and can conclude no significant difference among the three populations. - We should not reject \( H_0 \) and cannot conclude a significant difference among the means. - We should reject \( H_0 \) and cannot conclude a significant difference among the means. - We should reject \( H_0 \) and conclude a significant difference among the populations.This exercise requires understanding and calculating the ANOVA components, emphasizing statistical analysis and inference. The image shows a section of an educational statistical analysis problem related to ANOVA (Analysis of Variance) testing. Here's a detailed transcription and explanation of the content:---**(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 | | | || 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.- \( \bigcirc \) We should not reject \( H_0 \) and therefore can conclude that there is a significant difference among the means of the three populations.- \( \bigodot \) We should not reject \( H_0 \) and therefore cannot conclude that there is a significant difference among the means of the three populations. (selected)- \( \bigcirc \) We should reject \( H_0 \) and therefore cannot conclude that there is a significant difference among the means of the three populations.- \( \bigcirc \) We should reject \( H_0 \) and therefore can conclude that there is a significant difference among the means of the three populations. (selected)**(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 \(\bigvee\)/less than \(\bigwedge\)] the significance level we [should not/should] reject \( H_0 \) and conclude that there [is/is not] sufficient evidence in the data to suggest a significant difference among the mean ACT scores of the three majors.---**Additional Information:**- **ANOVA Table Explanation:** The table is used to compare variance across different groups to determine if there are statistically significant differences between their means. Each row refers to different sources of variability (e.g., Between Treatments, Within Treatments, Total).- **Hypothesis Testing:** Here, \( H

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 Sample Variance (a) Compute the overall sample mean . 29.5 x Between Treatments Within Treatments 12 Total 26 17 Major Finance Accounting 9 23 6 11 (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 25 11 (c) Using a 0.01, determine the critical value of F. (Round your answer to two decimal places.)

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 Sample Variance (a) Compute the overall sample mean . 29.5 x Between Treatments Within Treatments 12 Total 26 17 Major Finance Accounting 9 23 6 11 (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 25 11 (c) Using a 0.01, determine the critical value of F. (Round your answer to two decimal places.)

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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