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The ref. used by UCSC Physics is An Intro. to Error Analysis
(John R. Taylor) A thorough use is required by all majors in the
Advanced Lab. They get tested! I used the ancient bible The
Atomic Nucleus It has a number of counting examples (I think,
including how to "deal" with short 1/2 life nuclei.) (Robley D. Evans)
There are details I skipped, such as bins should be combined so that
there are a min of about five in each, etc.
bc
P.s. Do get your students to use (early and often) the Chi Square test.
brian whatcott wrote:
At 11:09 3/23/00 -0600, Glenn Carlson wrote:
>There is every reason to expect your data to fit a binomial
>distribution since it is the correct distribution. However, as Mr.
>Cleyet correctly points out, the Poisson distribution is more useful
>here because of the huge number of nuclei in your sample (on the order
>of 10^23) and the virtually zero probability that any one nucleus will
>decay during the counting interval.>//// As you can see
>in the table below, your data with a 0.5 second counting interval fits
>a Poisson distribution very well. I leave it to you and your students
>to analyze your data with a Gaussian distribution.
>
#counts #times c*t c! P(k;mu(c)) Expected #times = %diff =
(c) (t) (Poisson) P(k;mu(c))*sum(c*t) |Exp-meas|/Exp*1000 3321 0 1 0.109586319 3294.712675
/////////
sum(t) = 30065
sum(c*t) = 66475mean(c) = mu(c) = 2.211042741
>A final note. Remember to keep in mind that your measured count rate
>is not the same thing as the decay rate of your sample.....
>Glenn A. Carlson, P.E.Hmmm...it seems we can all learn a little something from this
puzzle of Ludwik's.
For example, in Glenn's working above, it would be better to
say that 2.211 is his *estimate* of the mean.Using my (incomparable?) least squares method, I see that it is more
likely to be 2.212 +- 0.005 in round numbers - speaking of which,
it is less than pukka to be quoting 10 places of precision anywhere
in this table: this is statistics, not quantum chromodynamics! :-)brian whatcott <inet@intellisys.net>
Altus OK