To calculate the F value using the provided ANOVA table, follow these steps:
### Step-by-Step Solution
1. Identify the relevant information from the ANOVA table:
- Degrees of Freedom (df):
- Within: [tex]\( df_{within} = 145 \)[/tex]
- Between: [tex]\( df_{between} = 4 \)[/tex]
- Sum of Squares (SS):
- Within: [tex]\( SS_{within} = 6525 \)[/tex]
- Between: [tex]\( SS_{between} = 540 \)[/tex]
- Mean Squared (MS):
- Within: [tex]\( MS_{within} = 45 \)[/tex]
- Between: [tex]\( MS_{between} = 135 \)[/tex]
2. Formula for the F value:
[tex]\[
F = \frac{MS_{between}}{MS_{within}}
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
F = \frac{135}{45}
\][/tex]
4. Calculate the F value:
[tex]\[
F = \frac{135}{45} = 3.0
\][/tex]
### Summary
Using the provided data:
- The F value is calculated as [tex]\( F = 3.0 \)[/tex].
This result indicates the ratio of the mean squared between groups to the mean squared within groups, which is used in hypothesis testing to determine if there are any statistically significant differences between group means in an ANOVA analysis.
