Questions: x̄D= Person (Pair) Pre-Test Post-Test XD ------------ 1 4 7 3 2 6 10 4 3 5 6 1 4 7 11 4 5 3 5 2

Solution Steps

We are given the pre-test and post-test scores for five individuals. The differences \( X_D \) are calculated as follows:

\[ X_D = \text{Post-Test} - \text{Pre-Test} \]

The calculated differences for each person are:

• Person 1: \( 7 - 4 = 3 \)
• Person 2: \( 10 - 6 = 4 \)
• Person 3: \( 6 - 5 = 1 \)
• Person 4: \( 11 - 7 = 4 \)
• Person 5: \( 5 - 3 = 2 \)

Thus, the differences are \( X_D = [3, 4, 1, 4, 2] \).

To find the mean \( \bar{x}_D \) of the differences \( X_D \), we use the formula:

\[ \bar{x}_D = \frac{\sum_{i=1}^N x_i}{N} \]

Where \( N \) is the number of pairs (in this case, \( N = 5 \)) and \( \sum_{i=1}^N x_i \) is the sum of the differences:

\[ \sum_{i=1}^5 X_D = 3 + 4 + 1 + 4 + 2 = 14 \]

Now, substituting into the mean formula:

\[ \bar{x}_D = \frac{14}{5} = 2.8 \]

Final Answer