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Additional info for Distriburions And Fourier Transforms. Lectures Notes. Winter term 2001-2002
The standard uncertainty uX is an estimate of the standard deviation of the parent population for the distribution of X considering the combination of all the errors affecting the measured value X. We do not know what the distribution will be when we combine the random errors with the systematic errors; however, a concept called the central limit theorem allows us to make a Gaussian (normal) assumption for X in many cases. The central limit theorem states that if X is not dominated by a single error source but instead is affected by multiple, independent error sources, then the resulting distribution for X will be approximately normal .
107, June 1985, pp. 161–164. 7. Moffat, R. , “Contributions to the Theory of Single-Sample Uncertainty Analysis,” Journal of Fluids Engineering, Vol. 104, June 1982, pp. 250–260. 8. Moffat, R. , “Using Uncertainty Analysis in the Planning of an Experiment,” Journal of Fluids Engineering, Vol. 107, June 1985, pp. 173–178. 9. Moffat, R. , “Describing the Uncertainties in Experimental Results,” Experimental Thermal and Fluid Science, Vol. 1, Jan. 1988, pp. 3–17. 10. Nikuradse, J. “Stromugsgestze in Rauhen Rohren,” VDI Forschungsheft, No.
25◦ F is taken. Within what range about this measurement will the parent population mean μT fall with 95% confidence (20:1 odds)? Solution (a) From Eq. 19), the interval defined by T ± t95 sT where t95 sT t95 sT = √ N will include μT with 95% confidence. 2. 04 F should include μT with 95% confidence. 11, we note that μT is the biased mean value and would only correspond to the true temperature Ttrue if the systematic error (bias) in the temperature measurements were zero. Also note the commonsense approach used in rounding off the final number for the confidence interval.