Please complete all parts Student: Kevin Burke Date: 02/19/18 Instructor: Budhin

Question

Please complete all parts

Student: Kevin Burke Date: 02/19/18 Instructor: Budhinath Padhy Course: Spring 2018 - Math 258 Assignment: Section 11.2 Homework Print 6. 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 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 measurements Note A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers 1 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 The upper bound is (Round to the nearest tenth as needed.) State the appropriate conclusion. Choose the correct answer below () There is sufficient evidence to conclude that the two indenters produce different hardness readings There is insufficient evidence to conclude that the two indenters produce different hardness readings 1: Data Table Specimen 1 2 3 4 5 6 78 9 Steel ball 50 57 61 70 68 54 65 51 53 Diamond 52 55 63 74 69 56 68 51 56

Explanation / Answer

The statistical software output for this problem is:

Paired T confidence interval:
D = 1 - 2 : Mean of the difference between Diamond and Steel Ball
95% confidence interval results:

Hence,

95% confidence interval will be:

Lower bound = 0.3

Upper bound = 3.1

Conclusion: Option A is correct.

Difference Mean Std. Err. DF L. Limit U. Limit Diamond - Steel Ball 1.6666667 0.60092521 8 0.28093066 3.0524027

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