To determine if there is a significant difference between the mean age of marriage across the three racial groups, we use an Analysis of Variance (ANOVA). The ANOVA test involves calculating the F statistic, which compares the mean square between the groups to the mean square within the groups.
Here's the step-by-step solution to calculate the F statistic:
1. Identify the given values:
- Mean square between groups ([tex]\(MS_{between}\)[/tex]): 313.01
- Mean square within groups ([tex]\(MS_{within}\)[/tex]): 36.87
2. Calculate the F statistic:
- The formula for the F statistic in ANOVA is:
[tex]\[
F = \frac{MS_{between}}{MS_{within}}
\][/tex]
3. Insert the given values into the formula:
- Substitute [tex]\(MS_{between} = 313.01\)[/tex] and [tex]\(MS_{within} = 36.87\)[/tex] into the formula:
[tex]\[
F = \frac{313.01}{36.87}
\][/tex]
4. Compute the result:
- Performing the division gives:
[tex]\[
F \approx 8.49
\][/tex]
Hence, the F statistic is approximately 8.49.
In summary, the calculations show that the F statistic value, which allows us to determine if the variances between groups are significantly different from the variances within groups, is approximately 8.49. This value can then be compared to a critical value from the F-distribution table to make a decision regarding the null hypothesis.
