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.

Specimen   Steel ball   Diamond
1   50   52
2   57   56
3   61   61
4   70   74
5   68   69
6   54   55
7   65   68
8   51   51
9   53   56

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.)

Answer 1

hii.. there is same result from R software. you can use - 6.3, 9.3). i have verified the explanation and also uploading with them.