The article “Calibration of an FTIR Spectrometer” (P. Pankratz, Statistical Case Studies for Industrial and Process Improvement, SIAM-ASA, 1997: 19-38) describes the use of a spectrometer to make five measurements of, the carbon content (in ppm) of a certain silicon-wafer whose true carbon content was known to be 1.1447 ppm. The measurements were 1.0730, 1.0825, 1.0711,1.0870, and 1.0979.

a. Is it possible to estimate the uncertainty in these measurements? If so, estimate it. If not, explain why not.

b. Is it possible to estimate the bias in these measurements? If so, estimate it. If not, explain why not.

Step 1 of 3:

Here an article describes the use of a spectrometer to make 5 measurements of, the carbon content was known to be 1.1447ppm. The measurements are 1.0730, 1.0825,1.0711, 1.0870.

We have to check whether

Is it possible to estimate uncertainty of these measurements.Is it possible to estimate bias of these measurements.Step 2 of 3:

Yes , we can estimate the uncertainty with the standard deviation of 5 measurements.Let be the measurement of carbon content . first we have to find the sample mean.

=

= (1.0730+1.0825+1.0711+1.0870)

= 0.8627

So the uncertainty will be

S =

=

= 0.7233 .

Therefore the uncertainty of the measurements is 0.7233 .