The Noise Function

Sometimes it is useful to be able to alter the results of a simulated experiment by building random errors into the data set at a controlled level. 

This can be easily and conveniently accomplished with the QPRO random function. 

12-1 From a set of analyses for which we have calculated a mean, x, and a standard deviation, s, what can we say about the chances of the results of further experiments on the same sample giving the same value as x what is the probability of the value falling between x + ts and x - ts  

12-2 A series of samples taken from a single piece of Cu ore were found to have 0.412, 0.422, 0.409, 0.430, 0.417, 0.413, 0.433, 0.431, 0.422, and 0.429 %Cu. Should all 10 of these results be used in reporting the sample composition What is the range of values of %Cu for this sample to the 95% confidence level If it is known that the analytical method used here has a precision of 0.6 relative %, are the results indicative of sample homogeneity  

12-3 Equation 12-11 was developed to deal with random relative error (noise). Develop an appropriate equation suitable to generate random absolute errors at various levels. Use both to examine the absolute standard deviation of a measurement of mass of 0.2000 g of a substance whose purity is known to 1%, assuming a weighing error of + 0.0002 g. Obtain 20 values using randomization of each factor and 20 values with both factors employed. What are the standard errors of the resultant means  

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A random absolute error can be achieved by multiplying the expected random absolute error, e.g., 0.0002g in mass measurement by the noise function using P = 1. The expected relative error, in this case 1%, arising from uncertainties in purity, is obtained by multiplying the mass by the noise function where P=0.02. (See Figure 12.4) Hence W, the randomized mass is... 

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