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 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.

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?:

Data Table 1 Specimen 1 2 3 4 5 6 78 9 Steel ball 50 57 61 70 68 54 65 51 53 Diamond 52 56 61 74 69 55 68 51 56

Explanation / Answer

Solution:-

Xd = 1.4444 , Sd = 1.6667 , n =9 , df = n-1 = 8 t0.025 = 2.306

95% confidence interval for the difference measurements:

X +/- t *sd/sqrt(n) = 1.4444 +/- 2.306 *1.6667sqrt(9)

= (0.1632 , 2.7255)

  

Specimen 1 2 3 4 5 6 7 8 9 diamond 52 56 61 74 69 55 68 51 56 stell ball 50 57 61 70 68 54 65 51 53 difference 2 -1 0 4 1 1 3 0 3

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