The manufacturer of hardness testing equipment uses steel-ball indenters to pene
ID: 3159095 • 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 judge whether the two indenters result in different measurements, where the differences are computed as diamond minus steel ball'Explanation / Answer
The differences are
2
-1
0
3
1
1
3
0
3
Calculating the standard deviation of the differences (third column):
s = 1.414213562
Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 0.471404521
Calculating the mean of the differences (third column):
XD = 1.333333333
For the 0.95 confidence level,
alpha/2 = (1 - confidence level)/2 = 0.025
t(alpha/2) = 2.306004135
lower bound = [X1 - X2] - t(alpha/2) * sD = 0.246272559
upper bound = [X1 - X2] + t(alpha/2) * sD = 2.420394108
Thus, the confidence interval is
( 0.246272559 , 2.420394108 ) [ANSWER]
************************************************
As 0 is not inside the interval,
OPTION A: There is sufficient evidence to conclude that the two indenters produce different hardness readings. [ANSWER, A]
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