STATISTICS
This gives aχ^2 of 1.2 for one d.o.f and no evidence for the claim.31.15 As the distribution at each value ofsis Poisson, the best estimate of the
measurement error is the square root of the number of counts, i.e.
√
n(s). Linear
regression givesa=4. 3 ± 2 .1andb=10. 06 ± 0 .94.
(a) The cosmic ray background must be present, sincen(0)= 0 but its value of
about 4 is uncertain to within a factor 2.
(b) The correlation coefficient betweenaandbis− 0 .63. Yes; ifawere reduced
towards zero thenbwould have to be increased to compensate.
(c) Yes,χ^2 =4.9 for five d.o.f., which is almost exactly the ‘expected’ value,
neither too good nor too bad.31.17 a 1 =2. 02 ± 0. 06 ,a 2 =− 2. 99 ± 0. 09 ,a 3 =4. 90 ± 0 .10;r 12 =− 0 .60.
31.19 Note that|dF|=|dF′/F′^2 |and write
1+N 1 − 1
(N 2 −1)F′
as