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In: Statistics and Probability

A thermocouple is being calibrated with a well designed ice bath. The measurements are given in...

A thermocouple is being calibrated with a well designed ice bath. The measurements are given in the table to the right. Using any mathematical tool of your choice,the mean is .174 and standard deviation of the sample is .24228. I recommend excel for this problem and a simple example is included on the module for this class.

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

b) Assume you have corrected for the bias error and write an expression for the precision error in this sample. Use the formula T=X± ( 2.101)ST (95% ) where X is the sample mean (which will be 0 C after correction for the bias error in this case) ST is the sample standard deviation, and the coefficient 2.101 is a correction to the expression due to the limited amount of data. (Google “t-test” if you are not familiar with this procedure – if we 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 coefficient of the Standard Deviation, 2.101, is based on a test called a t-test and depends on the confidence interval and the number of measurements, which were 95% and 18 in that case. Assume that there are only 14 measurements, but you have exactly the same average and standard deviation that you calculated on the previous problem. Go to section 3.6.12 of the book referenced in problem 1, read that section if necessary, and determine what the coefficient should be for this smaller data set. (In other words, what should “2.101” be replaced with in this new data set with only 14 samples.)

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