Use the Minitab Display to Test the Indicated Claim

question 56

Multiple Choice

Use the Minitab display to test the indicated claim. A manager records the production output of three employees who each work on three different machines for three different days. The
Sample results are given below and the Minitab results follow. $\begin{array} { r r r c c } &&& { \text { Employee } } \\& & \text { A } & \text { B } & \text { C } \\& \text { I } & 16,18,19 & 15,17,20 & 14,18,16 \\\text { Machine } & \text { II } & 20,27,29 & 25,28,27 & 29,28,26 \\& \text { III } & 15,18,17 & 16,16,19 & 13,17,16\end{array}$

$\begin{array}{l}\text { Analysis of Variance Items }\\\begin{array} { l r r r } \text { SOURCE } & D F & S S & M S \\\text { MACHINE } & 2 & 588.74 & 294.37 \\\text { EMPLOYEE } & 2 & 2.07 & 1.04 \\\text { INTERACTION } & 4 & 15.48 & 3.87 \\\text { ERROR } & 18 & 98.67 & 5.48 \\\text { TOTAL } & 26 & 704.96 &\end{array}\end{array}$


Assume that the number of items produced is not affected by an interaction between employee and machine. Using a $0.05$ significance level, test the claim that the choice of employee has no effect on the number of items produced. What is the value of the test statistic, $F$ ?

• A) \(F = 0.1898\)
• B) \(F = 0.2687\)
• C) \(F = 5.2692\)
• D) \(F = 53.7172\)

---

Definitions:

Period Costs

Costs that are not tied directly to the production process and are expensed in the period they are incurred, such as selling and administrative expenses.

Product Costs

Costs that are directly linked to the creation of a product, including materials, labor, and overhead.

September

The ninth month of the Gregorian calendar.

Manufacturing Overhead Cost

All indirect costs associated with manufacturing, including indirect labor, materials, and expenses that cannot be directly attributed to a specific product.