The manufacturer of hardness testing equipment uses steel-ball indenters can be tested. Because of differences between the two types of indenters, it is suspected that the two methods will produce different hardness readings. The metal specimens to be tested are large enough so that two indentions can be made. Therefore, the manufacturer uses both indenters on each specimen and compares the hardness readings. Construct a 95% confidence interval to judge whether the two indenters result in different penetrate metal that is being tested. However, the manufacturer thinks it would be better to use a diamond indenter so that all types of metal measurements. Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. E Click the icon to view the data table. Construct a 95% confidence interval to judge whether the two indenters result in different measurements, where the differences are computed as 'diamond minus steel ball'. The lower bound is Data Table - X The upper bound is (Round to the nearest tenth as needed.) Specimen 1 4 6 8 Steel ball 50 57 61 70 68 54 65 51 53 Diamond 52 55 63 74 69 56 68 51 56

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### Hardeness Testing Equipment Analysis

#### Problem Description
The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate metal that is being tested. However, the manufacturer thinks it would be better to use a diamond indenter so that all types of metal can be tested. Because of differences between the two types of indenters, it is suspected that the two methods will produce different hardness readings. The metal specimens to be tested are large enough so that two indentations can be made. Therefore, the manufacturer uses both indenters on each specimen and compares the hardness readings.

#### Task
Construct a 95% confidence interval to judge whether the two indenters result in different measurements.

#### Considerations
- Differences between hardness readings for both indenters on each specimen are computed as 'diamond minus steel ball'.
- Normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.

#### Steps
1. **View the Data Table**: The data for both indenters and each specimen is collected in a table format.

#### Data Table:
| Specimen | Steel ball | Diamond |
|----------|------------|---------|
| 1        | 50         | 52      |
| 2        | 57         | 55      |
| 3        | 61         | 63      |
| 4        | 70         | 74      |
| 5        | 68         | 69      |
| 6        | 54         | 56      |
| 7        | 65         | 68      |
| 8        | 51         | 61      |
| 9        | 53         | 56      |

#### Confidence Interval Construction
- **Compute the differences**: Subtract the steel ball hardness readings from the diamond hardness readings for each specimen.
- **Calculate the mean** and **standard deviation** of these differences.
- Use the appropriate statistical methods to construct a 95% confidence interval.

#### Input Fields:
- Lower Bound
- Upper Bound

#### Goal
- Enter your answers for the lower and upper bounds in the edit fields and then click Check Answer.

### Calculation [Optional for Detailed Solution]
```markdown
To calculate the 95% confidence interval:
1. **Difference Calculation**: 
   - Specimen 1: \( 52 - 50 = 2 \)
   - Specimen 2: \( 55 -
Transcribed Image Text:### Hardeness Testing Equipment Analysis #### Problem Description The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate metal that is being tested. However, the manufacturer thinks it would be better to use a diamond indenter so that all types of metal can be tested. Because of differences between the two types of indenters, it is suspected that the two methods will produce different hardness readings. The metal specimens to be tested are large enough so that two indentations can be made. Therefore, the manufacturer uses both indenters on each specimen and compares the hardness readings. #### Task Construct a 95% confidence interval to judge whether the two indenters result in different measurements. #### Considerations - Differences between hardness readings for both indenters on each specimen are computed as 'diamond minus steel ball'. - Normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. #### Steps 1. **View the Data Table**: The data for both indenters and each specimen is collected in a table format. #### Data Table: | Specimen | Steel ball | Diamond | |----------|------------|---------| | 1 | 50 | 52 | | 2 | 57 | 55 | | 3 | 61 | 63 | | 4 | 70 | 74 | | 5 | 68 | 69 | | 6 | 54 | 56 | | 7 | 65 | 68 | | 8 | 51 | 61 | | 9 | 53 | 56 | #### Confidence Interval Construction - **Compute the differences**: Subtract the steel ball hardness readings from the diamond hardness readings for each specimen. - **Calculate the mean** and **standard deviation** of these differences. - Use the appropriate statistical methods to construct a 95% confidence interval. #### Input Fields: - Lower Bound - Upper Bound #### Goal - Enter your answers for the lower and upper bounds in the edit fields and then click Check Answer. ### Calculation [Optional for Detailed Solution] ```markdown To calculate the 95% confidence interval: 1. **Difference Calculation**: - Specimen 1: \( 52 - 50 = 2 \) - Specimen 2: \( 55 -
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