facturer 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 he 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 imen and compares the hardness readings. Construct a 95% confidence interval to judge whether the two indenters result in different measurements. mal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. the icon to view the data table. a 95% confidence interval to judge whether the two indenters result in different measurements, where the differences are computed as 'diamond minus steel ball. bound is bound is Data table the nearest tenth as needed.) Specimen 1 Steel ball Diamond 2 3 4 7 9 51 57 61 71 68 54 65 51 53 ne solve this View an example Get more help - Clear all Check answer 53 55 63 74 69 55 68 51 56

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**Understanding Confidence Intervals in Material Testing**

In the field of material testing, manufacturers often use hardness testing equipment with steel-ball indenters to test the penetration of metals. There is a proposal to use diamond indenters, which may offer more comprehensive testing across various metal types. Due to potential differences between steel-ball and diamond indenters, it is hypothesized that they might yield varied hardness readings.

To explore this, a 95% confidence interval is constructed to determine if these indenters indeed produce significantly different measurements. This analysis involves metal specimens that are sufficiently large for both indentations. The goal is to compare the hardness readings obtained from both indenters.

**Data Table Explanation:**

A data table is provided, showing hardness readings for nine specimens using both steel-ball and diamond indenters. The values are as follows:

- **Specimen 1:** Steel ball - 51, Diamond - 53
- **Specimen 2:** Steel ball - 57, Diamond - 55
- **Specimen 3:** Steel ball - 71, Diamond - 63
- **Specimen 4:** Steel ball - 68, Diamond - 74
- **Specimen 5:** Steel ball - 54, Diamond - 69
- **Specimen 6:** Steel ball - 54, Diamond - 55
- **Specimen 7:** Steel ball - 51, Diamond - 68
- **Specimen 8:** Steel ball - 53, Diamond - 51
- **Specimen 9:** Steel ball - 51, Diamond - 56

The differences between the diamond and steel-ball readings are calculated for each specimen, serving as the basis for constructing the confidence interval.

**Task: Constructing Confidence Interval**

Construct a 95% confidence interval to determine whether the two indenters give different results. The difference is calculated as "diamond minus steel ball."

- **Lower Bound:** [Enter value]
- **Upper Bound:** [Enter value]

Round the results to the nearest tenth as needed.

This exploration assists in understanding the statistical analysis of material testing and improves testing protocols by ensuring more accurate and reliable measurements.
Transcribed Image Text:**Understanding Confidence Intervals in Material Testing** In the field of material testing, manufacturers often use hardness testing equipment with steel-ball indenters to test the penetration of metals. There is a proposal to use diamond indenters, which may offer more comprehensive testing across various metal types. Due to potential differences between steel-ball and diamond indenters, it is hypothesized that they might yield varied hardness readings. To explore this, a 95% confidence interval is constructed to determine if these indenters indeed produce significantly different measurements. This analysis involves metal specimens that are sufficiently large for both indentations. The goal is to compare the hardness readings obtained from both indenters. **Data Table Explanation:** A data table is provided, showing hardness readings for nine specimens using both steel-ball and diamond indenters. The values are as follows: - **Specimen 1:** Steel ball - 51, Diamond - 53 - **Specimen 2:** Steel ball - 57, Diamond - 55 - **Specimen 3:** Steel ball - 71, Diamond - 63 - **Specimen 4:** Steel ball - 68, Diamond - 74 - **Specimen 5:** Steel ball - 54, Diamond - 69 - **Specimen 6:** Steel ball - 54, Diamond - 55 - **Specimen 7:** Steel ball - 51, Diamond - 68 - **Specimen 8:** Steel ball - 53, Diamond - 51 - **Specimen 9:** Steel ball - 51, Diamond - 56 The differences between the diamond and steel-ball readings are calculated for each specimen, serving as the basis for constructing the confidence interval. **Task: Constructing Confidence Interval** Construct a 95% confidence interval to determine whether the two indenters give different results. The difference is calculated as "diamond minus steel ball." - **Lower Bound:** [Enter value] - **Upper Bound:** [Enter value] Round the results to the nearest tenth as needed. This exploration assists in understanding the statistical analysis of material testing and improves testing protocols by ensuring more accurate and reliable measurements.
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