Refer to the following partial ANOVA results from Excel (some information is missing). $$\begin{array} { | l | c | c | c | c | c | c | }
\hline \text { Source of Variation } & \text { SS } & d f & M S & F & P \text {-value } & F \text { crit } \
\hline \text { Between groups } & & & 210.2778 & & 0.064139 & \
\hline \text { Within groups } & 1483 & & 74.15 & & & \
\hline \text { Total } & 2113.833 & & & & & \
\hline
\end{array}$$ The critical value of F at ? = 0.05 is:
A)1.645.
B)2.84.
C)3.10.
D)4.28.

Question

Refer to the following partial ANOVA results from Excel (some information is missing). $$\begin{array} { | l | c | c | c | c | c | c | } 
\hline \text { Source of Variation } & \text { SS } & d f & M S & F & P \text {-value } & F \text { crit } \
\hline \text { Between groups } & & & 210.2778 & & 0.064139 & \
\hline \text { Within groups } & 1483 & & 74.15 & & & \
\hline \text { Total } & 2113.833 & & & & & \
\hline
\end{array}$$ The critical value of F at ? = 0.05 is:
A)1.645.
B)2.84.
C)3.10.
D)4.28.

Quizplus · Accepted Answer

In order to find the critical value of F, we need to know the degrees of freedom for the between groups and within groups. From the ANOVA table, we can see that the total degrees of freedom is missing, but we can calculate it by adding the degrees of freedom for between groups and within groups: 
Total degrees of freedom = degrees of freedom between groups + degrees of freedom within groups
Total degrees of freedom = df between groups + df within groups
Total degrees of freedom = df between groups + (n – k)
where n is the total number of observations and k is the number of groups.

Since the ANOVA table only provides the degrees of freedom for the within groups (df within groups = n – k = ___), we need to calculate the degrees of freedom for the between groups:

df between groups = total degrees of freedom – df within groups 
df between groups = ___ – ___

Now, we can use the degrees of freedom for between groups and within groups to find the critical value of F at α = 0.05 using an F-table or calculator. With df between groups = ___ and df within groups = ___, we find that the critical value of F at α = 0.05 is approximately 3.10. Therefore, the answer is C.

Refer to the Following Partial ANOVA Results from Excel (Some