https://file.aiquickdraw.com/mathbot/file/17304906208642vtufayw.jpg

Let's analyze and fill in the missing values in this ANOVA summary table.

### Given Information
- **Sum of Squares (S.S.):**
  - Between: 1475.88
  - Within: 1624.00
  - Total: 3099.88

- **Degrees of Freedom (d.f.):**
  - Between: 7
  - Within: 58
  - Total: 65

- **Mean Square (M.S.):**
  - Between: 210.84
  - Within: Missing (denoted by the key symbol)

### Calculations

#### 1. Mean Square (M.S.) for "Within"
The Mean Square for each category is calculated as:
\[
\text{M.S.} = \frac{\text{S.S.}}{\text{d.f.}}
\]

So, for the **Within** category:
\[
\text{M.S. (Within)} = \frac{1624.00}{58} = 28.00
\]

#### 2. F-Ratio (F)
The F-ratio is calculated as:
\[
F = \frac{\text{M.S. (Between)}}{\text{M.S. (Within)}}
\]

Substituting the values:
\[
F = \frac{210.84}{28.00} = 7.53
\]

### Completed ANOVA Table
The missing values are:

- **M.S. (Within)** = 28.00
- **F** = 7.53

So the completed table is:

|             | S.S.   | d.f. | M.S.  | F    |
|-------------|--------|------|-------|------|
| Between     | 1475.88| 7    | 210.84| 7.53 |
| Within      | 1624.00| 58   | 28.00 |      |
| Total       | 3099.88| 65   |       |      |

Would you like further details or explanations on any part of this process?

### Related Questions
1. How is the F-ratio used to determine statistical significance?
2. What do Sum of Squares values indicate in an ANOVA?
3. How can degrees of freedom affect the Mean Square value?
4. Why is the Total S.S. the sum of Between and Within S.S.?
5. What are typical threshold values for the F-ratio in hypothesis testing?

### Tip
In ANOVA, higher F-values typically indicate a greater likelihood that the group means differ significantly.

Fill in the missing values for this ANOVA summary table:

Learn how to fill in missing values in an ANOVA table, including Sum of Squares (S.S.), Degrees of Freedom (d.f.), Mean Square (M.S.), and F-Ratio (F). This example shows calculations for M.S. within and F-ratio for between-group comparison, with values provided for between, within, and total categories.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation