Use the Minitab Display to Test the Indicated Claim Assume That the Number of Items Produced Is Not Affected

question 156

Essay

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. $$\begin{array}{l}\begin{array} { c c c c c } & { \text { Employee } } \\& & \text { A } & \text { B } & \text { C } \\\text { Machine } & \text { I } & 23,27,29 & 30,27,25 & 18,20,22 \\& \text { II } & 25,26,24 & 24,29,26 & 19,16,14 \\& \text { III } & 28,25,26 & 25,27,23 & 15,11,17\end{array}\\\\\text { ANALYSIS OF VARIANCE ITEMS }\\\\\begin{array} { l r r r } \text { SOURCE } & \text { DF } & { \text { SS } } & { \text { MS } } \\\text { MACHINE } & 2 & 34.67 & 17.33 \\\text { EMPLOYEE } & 2 & 504.67 & 252.33 \\\text { INTERACTION } & 4 & 26.67 & 6.67 \\\text { ERROR } & 18 & 98.00 & 5.44 \\\text { TOTAL } & 26 & 664.00 &\end{array}\end{array}$$ 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 machine has no
effect on the number of items produced.

---

Definitions:

Sum Of The Squared Residuals

The total value obtained by summing the squares of the differences between observed and predicted values, used in statistical analysis to measure the fit of a model.

Data Points

Individual measurements or observations collected during data gathering.

Residual Term

The difference between observed values and the estimated values in a regression model.

Random Error

An error in measurement caused by unpredictable fluctuations in the variables being measured.