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 a very low morale and 10 a very high morale. Can we say that the new incentive plan did improve the morale of the workers? ( Use α=0.025 and do a sign test).

Question

Before 8 7 6 9 7 10 8 6
After 6 5 8 6 9 8 10 7
What is the value of n

Answer 1

To conduct a sign test for the paired data before and after the introduction of the incentive plan, we first need to determine the differences between the "After" and the "Before" scores for each worker.

Here are the scores:

• Before: 8, 7, 6, 9, 7, 10, 8, 6
• After: 6, 5, 8, 6, 9, 8, 10, 7

Now, we will compute the differences \(D = \text{After} - \text{Before}\):

1. For the first worker: \(6 - 8 = -2\)
2. For the second worker: \(5 - 7 = -2\)
3. For the third worker: \(8 - 6 = 2\)
4. For the fourth worker: \(6 - 9 = -3\)
5. For the fifth worker: \(9 - 7 = 2\)
6. For the sixth worker: \(8 - 10 = -2\)
7. For the seventh worker: \(10 - 8 = 2\)
8. For the eighth worker: \(7 - 6 = 1\)

Now we list the differences:

• \(D = -2, -2, 2, -3, 2, -2, 2, 1\)

Next, we will count the number of positive, negative, and zero differences. The positive differences (where morale increased) are \(2, 2, 2, 1\) and there are four positive differences.

The negative differences (where morale decreased) are \(-2, -2, -3, -2\) and there are four negative differences.

There are no zero differences in this data set.

Thus:

• Number of positive differences (\(n^+\)) = 4
• Number of negative differences (\(n^-\)) = 4
• Total number of pairs (\(n\)) = \(n^+ + n^- = 4 + 4 = 8\)

Therefore, the value of \( n \) is 8.