Based on the table provided and the question regarding the sum of squares for treatments and errors, the problem relates to ANOVA (Analysis of Variance).

Degrees of Freedom (DF)

1. Degrees of Freedom for Treatments (DF₁): The degrees of freedom for treatments is calculated as the number of groups (k) minus 1.

   • From the table, we can see three categories: Small Cap, Mid Cap, and Large Cap. Thus, there are 3 groups. $\text{DF}_{\text{treatments}} = k - 1 = 3 - 1 = 2$

2. Degrees of Freedom for Error (DF₂): The degrees of freedom for the error is calculated as the total number of observations (N) minus the number of groups (k).

   • To find the total number of observations (N), count all the entries in the table. There are 8 small-cap funds, 8 mid-cap funds, and 7 large-cap funds. So: $N = 8 + 8 + 7 = 23$ $\text{DF}_{\text{error}} = N - k = 23 - 3 = 20$

Thus, the degrees of freedom are:

• DF for treatments = 2
• DF for error = 20

Would you like a detailed explanation of ANOVA or the next steps in solving this problem?

Related Questions:

1. How is the F-ratio calculated in ANOVA?
2. What assumptions are required for conducting an ANOVA test?
3. What is the formula for sum of squares total in ANOVA?
4. How do you calculate the mean square for treatments and errors?
5. How do you interpret the results of an ANOVA test?

Tip:

When conducting ANOVA, ensure that the data meets the assumptions of normality, homogeneity of variances, and independence of observations.