A thermocouple is being calibrated with a well designed icebath. The measurements are given in the table to the right. Usingany mathematical tool of your choice,the mean is .174 and standarddeviation of the sample is .24228. I recommend excel for thisproblem and a simple example is included on the module for thisclass.

a) What is the bias error in this sample, assuming a perfect icebath?

b) Assume you have corrected for the bias error and write anexpression for the precision error in this sample. Use the formulaT=X± ( 2.101)ST (95% ) where X is the sample mean (which will be 0C after correction for the bias error in this case) ST is thesample standard deviation, and the coefficient 2.101 is acorrection to the expression due to the limited amount of data.(Google “t-test” if you are not familiar with this procedure – ifwe had an infinite amount of data, this value would be 1.96.)  

Test number Measurement C

1 0.220

2 0.280

3 0.190

4 0.510

5    -0.130

6 0.230

7 0.400

8 0.110

9 0.100

10    0.390

11 -0.090

12    0.490

13 0.250

14    0.550

15 0.100

16 -0.180

17 -0.250

18    -0.030

4) In the previous test you were given a formula: The coefficientof the Standard Deviation, 2.101, is based on a test called at-test and depends on the confidence interval and the number ofmeasurements, which were 95% and 18 in that case. Assume that thereare only 14 measurements, but you have exactly the same average andstandard deviation that you calculated on the previous problem. Goto section 3.6.12 of the book referenced in problem 1, read thatsection if necessary, and determine what the coefficient should befor this smaller data set. (In other words, what should “2.101” bereplaced with in this new data set with only 14 samples.)