A company wants to determine whether the average monthly sales differ among three different regions: North, South, and West. The company collects monthly sales data (in thousands of dollars) from four randomly selected stores in each region over the same month. Calculate the F-statistic given the Mean Square due to Treatments: MST = $226.6$ (variance between groups) and the Mean Square due to Error: MSE = $7.944$ (variance within groups).

• A. $7.94$
• B. $28.52$
• C. $226.6$
• D. $0.035$

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the problem. The goal is to calculate the F-statistic, which is used in ANOVA (Analysis of Variance) to determine if there are significant differences between group means. The formula for the F-statistic is F = MST / MSE, where MST is the Mean Square due to Treatments (variance between groups) and MSE is the Mean Square due to Error (variance within groups).
2. Step 2: Identify the given values. From the problem, we are provided with MST = 226.6 and MSE = 7.944. These values represent the variance between groups and the variance within groups, respectively.
3. Step 3: Write the formula for the F-statistic. Using MathML, the formula is: $F=\frac{\mathrm{MST}}{\mathrm{MSE}}$. This formula divides the variance between groups by the variance within groups.
4. Step 4: Substitute the given values into the formula. Replace MST with 226.6 and MSE with 7.944 in the formula: $F=\frac{226.6}{7.944}$.
5. Step 5: Perform the division to calculate the F-statistic. Divide 226.6 by 7.944 to obtain the F-statistic. This value will indicate whether the differences between the group means are statistically significant.