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Measurement and Analysis of Resistor Values and Muon Lifetimes

This document details the measurement of resistor values and the analysis of muon lifetimes. Initial findings showed a discrepancy in resistance measurements, highlighting the challenges of obtaining accurate statistics through fine binning. The muon lifetime study presents a Chi-squared analysis indicating potential issues with data validity. Despite these challenges, results indicate a muon lifetime of τ(μ) = 2.3 ± 0.6 μs. The note discusses finer statistical analysis and addresses the importance of proper data selection to avoid confounding results.

lucian-richardson
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Measurement and Analysis of Resistor Values and Muon Lifetimes

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  1. 8.13

  2. x

  3. Real life Part I Measure resistors UB9/12/06 Manufacturer: 5% 2.20 ± 0.01 k <R> = 2.178 ± 0.023 k OK Both histogram show the same data Finer binning sometimes confusing -> Lower statistic/bin

  4. Real Life Part II: Both 8.13 Groups ~ same Systematics of DVM-> small difference, both:gap Manufacturer 100 ± 5  Group1 9/10/04 what?? <R> = 103 ± ??  Not an independent sample!! Best ones were selected out (gap)!! Never a normal distribution. Variance can still be quoted ± 7  !!! Group1 9/10/04

  5. 8

  6. Gaussian errors Gaussian Shape? Poisson error

  7. Decays/s Theo 1 2 s log #/s log #/s Theo Theo Theo 100 10 1 100 10 1 1 2 s 1 2 s 1 2s Back to our measurements of the muon lifetime: 2/dof = 18.1 for  = 8 - 2, exponential (hypothesis) or data doubtful. Note: the first point is >4 off the curve ~16 to 2. Was started to late, delete. NOW () = 2.050.03 s good! 2/dof = 0.3 for  =4-2, which is fine. Result: ()= 2.30.6 s not accurate - nobody cares

  8. More Bevington, Taylor…. Let’s go!

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