Assignment 1 - Solutions

note: there were several different sets of data, the following is one example

 
(a) The following is a typical set of data for determining a calibration line.  For the data, determine the following quantities: Sxx, Syy, Sxy, Sr, the slope m, and the intercept b of the best fit line.  You can determine these numbers any way you like (by hand or by spreadsheet), but if done by spreadsheet, include the formulae used in your report.

concenstration (ppm) instrument reading
0.0
5.0
10.0
15.0
20.0
unk
0.06
1.48
2.28
3.98
4.61
3.67
 
Sol'n Sxx = 02 + 52 + 102 + 152 + 202 + (0 + 5 + 10 + 15 + 20)2/5  =  250  (or use spreadsheet formula)
similarly, Sxy = 58;  ; Syy = 13.68328

slope = m = Sxy/Sxx = 0.232

mean(x) = 10;  mean(y) = 2.482
intercept = b = mean(y) - m*mean(x) = 0.162
 
(b) Determine the concentration of the unknown sample and give the confidence interval for the number.
 
Sol'n The x value for the unknown y is:
[unk] = (y - b)/m = (3.67 - 0.162) / 0.232 = 15.1206....

Sr = 0.275245...
Su = 1.355....

Therefore, the unknown has a concentration of 15 +/- 1 ppm.

Also acceptable: 15.1 +/- 1.4 ppm.


 

Last updated, February 4, 2005
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