a) Compute the overall sample mes 29.5 X (b) Set up the ANOVA table for this Source of Variation Between Treatments Within Treatments Total (c) Using a = 0.01, determine the (d) Using the critical value approa O We should not reject Ho ar
a) Compute the overall sample mes 29.5 X (b) Set up the ANOVA table for this Source of Variation Between Treatments Within Treatments Total (c) Using a = 0.01, determine the (d) Using the critical value approa O We should not reject Ho ar
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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Question
Transcribed Image Text:Certainly! Below is the transcription of the text in the image, along with explanations of the tables included.
---
**Text:**
You may need to use the appropriate technology to answer this question. Information regarding the three samples is shown below.
| Sample Size | Management | Finance | Accounting |
|-------------|------------|---------|------------|
| Sample Size | 12 | 9 | 23 |
| Sample Mean | 25 | 21 | 23 |
(a)
(c) Using α = 0.01, determine the critical value of F. (Round your answer to two decimal places.)
(b) Compute the overall sample mean \(\bar{x}\).
(d) Set up the ANOVA table for this problem including the SS (sum of squares) 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 | | | | |
(e) Using the critical value approach, test to determine whether there is a significant difference in the means of the populations.
- We should not reject \(H_0\), and therefore cannot conclude that there is a significant difference in the means of the three populations.
- We should reject \(H_0\), and therefore can conclude that there is a significant difference in the means of the three populations.
---
**Explanation of Graphs/Diagrams:**
1. **Table of Sample Information:**
- The table shows sample sizes and means for three different groups: Management, Finance, and Accounting. The Management sample has a size of 12 and a mean of 25. The Finance sample has a size of 9 and a mean of 21. The Accounting sample has a size of 23 and a mean of 23.
2. **ANOVA Table:**
- The ANOVA table is set up to calculate the variance between treatments and within treatments. It includes columns for the Source of Variation, Sum of Squares, Degrees of Freedom, Mean Square, and F statistic. The entries in this table need to be calculated as part of the problem.
Overall, this setup is for conducting an ANOVA test to determine if there is a statistically significant difference between the means of the
Transcribed Image Text:**Transcription for Educational Website:**
---
**Step-by-Step ANOVA Analysis**
1. **Setup ANOVA Table:**
- Identify the sources of variation, including Between Treatments and Total.
- Determine the sum of squares, degrees of freedom, and mean squares for each source.
2. **Critical Value Calculation:**
- Using a significance level (\(\alpha\)) of 0.01, find the critical value for the F-test. Round this value to two decimal places.
3. **F-value and P-value Determination:**
- Calculate the F-statistic to two decimal places.
- Compute the p-value for the test. Round this value to four decimal places.
4. **Hypothesis Testing Decision:**
- Option (a): Reject \(H_0\) if there is not sufficient evidence of a significant difference among the population means.
- Option (b): Fail to reject \(H_0\) if a significant difference exists.
**Conclusion:**
- Using the p-value and comparing it with the significance level, make a final decision to either reject or fail to reject the null hypothesis. Support the conclusion based on whether the data suggest a significant difference among the population means.
---
**Diagram Description:**
The image contains an ANOVA table with sections for the sources of variation, sum of squares, degrees of freedom, mean squares, and F-statistics. The table is partially filled and is intended to guide users on how to complete an ANOVA analysis step-by-step, relevant for comparing multiple population means.
Expert Solution
Step 1
The information regarding the ACT scores of samples of students in three different majors is given below:
| Sample | Management | Finance | Accounting |
| Sample size | 12 | 9 | 11 |
| Average | 26 | 23 | 25 |
| Sample variance | 17 | 6 | 11 |
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Solved in 6 steps with 2 images
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