The manufacturer of hardness testing equipment uses steel-ball Indenters to pene

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 dlamond indenter so that all types of metal can be tested. Because of the differences between the two types of indenters, it is suspected that the two methods will produce different hardness readings. The metal speclmens to be tested are large enough that the two Indentions can be made. Therefore, the manufacturer uses both indenters on each specimen and compares the hardness readings. The data are displayed in the table Specimen 1 2 3 456 7 8 9 Steel Ball 51 57 61 71 68 54 65 51 53 Diamond 53 55 63 74 69 56 68 51 56 Construct a 95% confidence interval of the difference between the two readings, where d steel ball - diamond. O (-2.837,-0.2744) O (0.2744, 2.837) (-64.816,-53.184) 0 (53.184, 64.816) enovO

Explanation / Answer

solution:-
given that d = steel ball - diamond
the vaues are
-2,2,-2,-3,-1,-2,-3,0,-3
mean = ?1.5556
standard deviation = 1.6667
95% confidence with df = 9 - 1 = 8 is t = 2.306
confidence interval formula
=> x +/- t * s / sqrt(n)
=> ?1.5556 +/- 2.306 * 1.6667 /sqrt(9)
=> (-2.837 , -0.2744)

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