Math  /  Data & Statistics

QuestionQuestion 4
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Fill in the missing values for this ANOVA summary table: \begin{tabular}{|c|c|c|c|c|c|c|} \hline & S.S. & \multicolumn{2}{|c|}{d.f.} & & M.S. & F \\ \hline Between & & 7 & \checkmark & & & 3.353 \\ \hline Within & 2325 & 93 & \checkmark & 2 & & \\ \hline TOTAL & & 100 & & & & \\ \hline \end{tabular}
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Studdy Solution

STEP 1

1. The ANOVA table is structured with columns for Sum of Squares (S.S.), degrees of freedom (d.f.), Mean Square (M.S.), and F-ratio (F).
2. The relationship between S.S., d.f., and M.S. is given by M.S.=S.S.d.f. \text{M.S.} = \frac{\text{S.S.}}{\text{d.f.}} .
3. The F-ratio is calculated as F=M.S. BetweenM.S. Within F = \frac{\text{M.S. Between}}{\text{M.S. Within}} .
4. The total degrees of freedom is the sum of the "Between" and "Within" degrees of freedom.

STEP 2

1. Calculate the missing S.S. for the "Between" group.
2. Calculate the missing M.S. for the "Between" group.
3. Calculate the missing S.S. for the "TOTAL" group.
4. Verify calculations and fill in the table.

STEP 3

Calculate the missing S.S. for the "Between" group using the formula for M.S.:
M.S. Between=S.S. Betweend.f. Between \text{M.S. Between} = \frac{\text{S.S. Between}}{\text{d.f. Between}}
Given M.S. Between=3.353 \text{M.S. Between} = 3.353 and d.f. Between=7 \text{d.f. Between} = 7 ,
S.S. Between=3.353×7=23.471 \text{S.S. Between} = 3.353 \times 7 = 23.471

STEP 4

The M.S. for the "Within" group is given as 25, which is consistent with the provided data.

STEP 5

Calculate the missing S.S. for the "TOTAL" group:
The total degrees of freedom is the sum of the "Between" and "Within" degrees of freedom:
d.f. TOTAL=7+93=100 \text{d.f. TOTAL} = 7 + 93 = 100
The S.S. for the "TOTAL" group is the sum of the "Between" and "Within" S.S.:
S.S. TOTAL=23.471+2325=2348.471 \text{S.S. TOTAL} = 23.471 + 2325 = 2348.471

STEP 6

Verify calculations and fill in the table:
\begin{tabular}{|c|c|c|c|c|c|c|} \hline & S.S. & \multicolumn{2}{|c|}{d.f.} & & M.S. & F \\ \hline Between & 23.471 & 7 & \checkmark & & 3.353 & 3.353 \\ \hline Within & 2325 & 93 & \checkmark & 25 & & \\ \hline TOTAL & 2348.471 & 100 & & & & \\ \hline \end{tabular}
The completed ANOVA table is verified and filled in.

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