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Unformatted text preview: For your use in Senior Project! • Assume you timed 9 cycles (first example). • Standard error of the average for each element: • Where = standard deviation of the distribution of averages. = standard deviation of the universe for a given element. N = actual number of observations made. δ δ X N = ′ δ X ′ δ Equation (1) Equation (1) Conducting a Sampling Study • By definition, σ is the rootmeansquare deviation of observed readings from their average: • Where: X = each stopwatch reading (of a particular element). = average of all the clock times of an element. ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 2 1 2 ... N X X X X X X X X X X N N N δ  +  + +   = = =  ∑ ∑ X Equation (2) Equation (2) Conducting a Sampling Study • Since • Then • Combining Equations (1) and (3): • where N’ is the required number of observations for a specified confidence and accuracy . X X N = ∑ ( 29 { } δ =  =  ∑ ∑ ∑ ∑ X N X N N X X 2 2 2 2 2 1 ( 29 ( 29 δ X N N X X N =  ′ ∑ ∑ 1 2 2 Equation (3) Equation (3) Conducting a Sampling Study • Decision now must be made to establish a level of confidence and accuracy. • The most common in time study are: confidence level = C.L. = 95% accuracy = α = ± 5% or ± 10% Conducting a Sampling Study • 95 % C.L. → in at least 95 out of 100 samples, the sample mean time will be within ± 5% of the true mean. • That is, the interval of the sample mean ± 5% will contain the true mean 95% of the time. Conducting a Sampling Study • Sample Size: – Accuracy: Relative (S) versus Absolute (A): • If the mean percent occurrence = 40%, then – a 10% relative accuracy (relative to the mean) is (.1)(.4) = 4% absolute accuracy. – a 20% relative accuracy is (.2)(.4)=8% absolute accuracy. – a 30% relative accuracy is (.3)(.4) = 12% absolute accuracy, etc. ∴ A = S*p • The distinction is very important! Need to use absolute accuracy in calculations, but most laypersons think in terms of relative accuracy (especially management!). p Conducting a Sampling Study • Accuracy desired, confidence desired, and data variability are related as follows: • A = – where: • A = absolute accuracy desired = precision = S ( ∑ X/N). • S = relative accuracy desired. • Z = # of standard deviations corresponding to the confidence desired. • = standard deviation of the population times. ' x z σ ' x σ Conducting a Sampling Study • Standard deviation of the population and the subsample times are related by: • where: – N’ = # of observations required to meet precision and accuracy criteria – = standard deviation of the subsample = (biased)....
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This note was uploaded on 06/14/2011 for the course HIST 1301 taught by Professor Gonzales during the Spring '11 term at The University of Texas at San Antonio San Antonio.
 Spring '11
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