Answer :
In this problem, we're dealing with one of the key concepts in statistics known as Analysis of Variance (ANOVA). ANOVA is used to compare the means of three or more samples to see if at least one of the sample means is significantly different from the others.
To calculate the F-ratio in an ANOVA, you divide the Mean Square Between (MSB) by the Mean Square Within (MSW). The formula for the F-ratio is given by:
[tex]F = \frac{\text{MSB}}{\text{MSW}}[/tex]
Here, you have:
- MSB (Mean Square Between) = 740
- MSW (Mean Square Within) = 210
Substituting these values into the formula, we get:
[tex]F = \frac{740}{210}[/tex]
Calculating this division gives:
[tex]F \approx 3.52[/tex]
Therefore, the F-ratio is approximately 3.52. This value helps in determining whether there are any statistically significant differences between the means of the groups being compared. If the F-ratio is significantly higher than the critical value from the F-distribution table for a given level of significance, we reject the null hypothesis that all group means are equal.
