Question

Management decided to introduce an incentive plan to try to increase the productivity in a small manufacturing plant. The morale of the workers was measured before and after the introduction of the new plan. A scale of 1 to 10 was used, where 1 is very low morale and 10 a very high morale. Can we say that the new incentive plan improve the morale of the workers? ( Sign test.


Before / Voor

8

7

6

9

7

10

8

6

After / Na

6

5

8

6

9

8

10

7



What is the value of n?

Answer 1

In a sign test, we compare paired observations to determine if there is a significant difference between them. In this case, we are comparing the morale scores of workers before and after the introduction of the incentive plan.

First, we need to calculate the differences for each pair of observations (After - Before) and then take the sign of those differences:

\[
\text{Before} / \text{After}
\begin{align*}
8 & / 6 & \Rightarrow & \quad 6 - 8 = -2 \quad (\text{negative}) \\
7 & / 5 & \Rightarrow & \quad 5 - 7 = -2 \quad (\text{negative}) \\
6 & / 8 & \Rightarrow & \quad 8 - 6 = +2 \quad (\text{positive}) \\
9 & / 6 & \Rightarrow & \quad 6 - 9 = -3 \quad (\text{negative}) \\
7 & / 9 & \Rightarrow & \quad 9 - 7 = +2 \quad (\text{positive}) \\
10 & / 8 & \Rightarrow & \quad 8 - 10 = -2 \quad (\text{negative}) \\
8 & / 10 & \Rightarrow & \quad 10 - 8 = +2 \quad (\text{positive}) \\
6 & / 7 & \Rightarrow & \quad 7 - 6 = +1 \quad (\text{positive}) \\
\end{align*}
\]

Now, we will count the number of positive and negative differences:

- Negative differences: 4 (from pairs 1, 2, 4, and 6)
- Positive differences: 4 (from pairs 3, 5, 7, and 8)

Next, we need to determine the value of \(n\), which is the total number of pairs for which we observe a difference (not equal to zero).

Since we have differences for all 8 pairs, \(n = 8\).

Thus, the value of \(n\) is **8**.