Random sampling from four normally distributed populations produced the following data: (You may find it useful to reference the E table.) A -5 -9 -9 Treatments B -5 -17 -10 -15 Grand mean SSTR MSTR C -20 -13. -4 -17 -10 D -12 picture Click here for the Excel Data File a. Calculate the grand mean. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) -19 -16 -12.07 b. Calculate SSTR and MSTR. (Round final answers to 4 decimal places.)
Random sampling from four normally distributed populations produced the following data: (You may find it useful to reference the E table.) A -5 -9 -9 Treatments B -5 -17 -10 -15 Grand mean SSTR MSTR C -20 -13. -4 -17 -10 D -12 picture Click here for the Excel Data File a. Calculate the grand mean. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) -19 -16 -12.07 b. Calculate SSTR and MSTR. (Round final answers to 4 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
Related questions
Question
![### Transcription for Educational Website
#### Step c.
**Calculate SSE and MSE.**
*Round final answers to 4 decimal places.*
| SSE | [Input Field] |
|-----|---------------|
| MSE | [Input Field] |
---
#### Step d.
**Specify the competing hypotheses in order to determine whether some differences exist between the population means.**
- \(H_0: \mu_A \geq \mu_B \geq \mu_C; \quad H_A: \text{Not all population means are equal.}\)
- \(H_0: \mu_A \leq \mu_B \leq \mu_C; \quad H_A: \text{Not all population means are equal.}\)
- \(H_0: \mu_A = \mu_B = \mu_C; \quad H_A: \text{Not all population means are equal.}\)
---
#### Step e-1.
**Calculate the value of the \(F(df_1, df_2)\) test statistic.**
*Round final answer to 3 decimal places.*
| Test statistic | [Input Field] |](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F21d4eb06-eaa2-4705-83a6-21563ae4212f%2F2c2103a5-8492-4ad9-8b30-d5d386e72e58%2F2acdzvt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Transcription for Educational Website
#### Step c.
**Calculate SSE and MSE.**
*Round final answers to 4 decimal places.*
| SSE | [Input Field] |
|-----|---------------|
| MSE | [Input Field] |
---
#### Step d.
**Specify the competing hypotheses in order to determine whether some differences exist between the population means.**
- \(H_0: \mu_A \geq \mu_B \geq \mu_C; \quad H_A: \text{Not all population means are equal.}\)
- \(H_0: \mu_A \leq \mu_B \leq \mu_C; \quad H_A: \text{Not all population means are equal.}\)
- \(H_0: \mu_A = \mu_B = \mu_C; \quad H_A: \text{Not all population means are equal.}\)
---
#### Step e-1.
**Calculate the value of the \(F(df_1, df_2)\) test statistic.**
*Round final answer to 3 decimal places.*
| Test statistic | [Input Field] |
Transcribed Image Text:**Title: Analysis of Variance (ANOVA) Example**
**Overview:**
This example demonstrates the calculation of the grand mean, and the sum of squares for treatment (SSTR) and mean square for treatment (MSTR) from samples drawn from four normally distributed populations. You may find it useful to reference the F table for further analysis.
**Data:**
The treatments and their corresponding data points are as follows:
| | Treatments |
|---|------------|
| | A | B | C | D |
| 1 | -5 | -5 | -20 | -12 |
| 2 | -9 | -17 | -13 | -19 |
| 3 | -9 | -10 | -4 | -16 |
| 4 | | -15 | -17 | |
| 5 | | | -10 | |
**Instructions:**
**a. Calculate the Grand Mean:**
- **Task:** Calculate the grand mean.
- **Note:** Negative values should be indicated by a minus sign. Round your answer to 2 decimal places.
- **Solution:**
Grand mean = -12.07
**b. Calculate SSTR and MSTR:**
- **Task:** Calculate SSTR (Sum of Squares for Treatments) and MSTR (Mean Square for Treatments).
- **Note:** Round final answers to 4 decimal places.
| | |
|---|---------|
| SSTR | |
| MSTR | |
**Graphical Elements:**
There are no graphs or diagrams accompanying this data; however, the data is presented in a tabular format for ease of analysis.
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