A manufacturer of hardness testing equipment employs 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 harness readings. The metal specimens to be tested are large enough so that two indentions can be made. Therefore, the maufacturer uses both indenters on each specimen and compares the hardness readings.
Specimen 1 2 3 4 5 6 7 8 9
Steel Ball 50 57 61 71 68 54 65 51 53
Diamond 52 56 61 74 69 55 68 51 56
1. ) Construct a 95% confidence interval for the mean difference of this data. (Use Diamond - Steel for differences)
Calculate the sum of the differences =
Calculate the sum of the individual differences squared =
Calculate d-bar: (Round to 1 decimal place)
Calculate the standard deviation of the differences: (Round to 1 decimal place)
Calculate E = (Round to 1 decimal place)
Confidence Interval is from to (Round to 1 decimal place)