The manufacturer of hardness testing equipment uses steel-ball indenters to pene
ID: 3049633 • Letter: T
Question
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. click the icon to view the data table. Construct a 95% confidence interval to udge whether the two indenters result in different measurements, where the differences are computed asdiamon minus steel ball' The lower bound is Data Table The upper bound is Round to the nearest tenth as needed.) Specimen 12 3 4 5 6 789 68 Enter your answer in the edit fields and then clickSteel ba 50 57 61 71 54 65 51 53 Diamond 52 55 63 74 69 55 68 51 56 4 partExplanation / Answer
Here aas the data is paired data for given 9 specimen.
The difference table is
Here average difference dbar = 1.4444
Paired data n = 9
Standard deviation of difference sd= 1.6667
Standard error of difference sed= 1.6667/sqrt(9) = 0.5556
95% confidence interval = dbar +- t0.05,8 sed = 1.4444 +- 2.306 * 0.5556 = (0.1633, 2.7256)
Lowe bound = 0.2
Upper bound = 2.7
Specimen Steel Ball Diamond Difference 1 50 52 2 2 57 55 -2 3 61 63 2 4 71 74 3 5 68 69 1 6 54 55 1 7 65 68 3 8 51 51 0 9 53 56 3 Average Difference 1.4444 Std. Dev. 1.6667Related Questions
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