Provide an appropriate response. Data sets A and B are dependent. Find a. 6.1 7.1 9.0 6.0 6.1 B 8.5 7.4 7.3 7.2 8.6 Assume that the paired data came from a population that is normally distributed. O 0.89 O -0.94 O 0.58 -0.76

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### Example of Paired Data Analysis

#### Problem Statement

Provide an appropriate response.

Data sets A and B are dependent. Find \(\overline{d}\).

```
     A: 6.1  7.1  9.0  6.0  6.1
     B: 8.5  7.4  7.3  7.2  8.6
```

Assume that the paired data came from a population that is normally distributed.

#### Choices

```
O  0.89
O -0.94
O  0.58
O -0.76
```

### Solution

1. **Calculate the differences (\(d\)) for each pair**:
   ```
   d = A - B
   For each pair:
     (6.1 - 8.5) = -2.4
     (7.1 - 7.4) = -0.3
     (9.0 - 7.3) =  1.7
     (6.0 - 7.2) = -1.2
     (6.1 - 8.6) = -2.5
   ```

2. **Find the mean of these differences**:
   ```
   \(\overline{d}\) = \(\frac{\sum d}{n}\)
   = \(\frac{-2.4 + (-0.3) + 1.7 + (-1.2) + (-2.5)}{5}\)
   = \(\frac{-4.7}{5}\)
   = -0.94
   ```

### Explanation

- The task is to find the mean difference between two sets of dependent data.
- Data set A: 6.1, 7.1, 9.0, 6.0, 6.1
- Data set B: 8.5, 7.4, 7.3, 7.2, 8.6
- The differences are calculated for each pair, and then the mean of these differences is found.

Thus, the correct answer is \(-0.94\).
Transcribed Image Text:### Example of Paired Data Analysis #### Problem Statement Provide an appropriate response. Data sets A and B are dependent. Find \(\overline{d}\). ``` A: 6.1 7.1 9.0 6.0 6.1 B: 8.5 7.4 7.3 7.2 8.6 ``` Assume that the paired data came from a population that is normally distributed. #### Choices ``` O 0.89 O -0.94 O 0.58 O -0.76 ``` ### Solution 1. **Calculate the differences (\(d\)) for each pair**: ``` d = A - B For each pair: (6.1 - 8.5) = -2.4 (7.1 - 7.4) = -0.3 (9.0 - 7.3) = 1.7 (6.0 - 7.2) = -1.2 (6.1 - 8.6) = -2.5 ``` 2. **Find the mean of these differences**: ``` \(\overline{d}\) = \(\frac{\sum d}{n}\) = \(\frac{-2.4 + (-0.3) + 1.7 + (-1.2) + (-2.5)}{5}\) = \(\frac{-4.7}{5}\) = -0.94 ``` ### Explanation - The task is to find the mean difference between two sets of dependent data. - Data set A: 6.1, 7.1, 9.0, 6.0, 6.1 - Data set B: 8.5, 7.4, 7.3, 7.2, 8.6 - The differences are calculated for each pair, and then the mean of these differences is found. Thus, the correct answer is \(-0.94\).
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