A new method for measuring the concentration of Pu 239 based on the registration

Question

A new method for measuring the concentration of Pu239based on the registration of -
particles and ?ssion-fragment tracts is studied. Test solutionmedia of various concentrations
are obtained, and each is split into two portions. Theconcentration of the ?rst portion
is determined using the new method; the second portion is measuredusing the standard
technique. It is thought that the new procedure tends to give ahigher average reading than
the standard technique. The data are as follows:

Concentration of PU239 (µ/ml)
Solution # New Old
1   3.78    3.35
2     3.58     3.60
3     3.77     3.41
4     3.82     3.69
5     3.67     3.48
6     3.66     3.50
7     3.48     3.33
8     3.63     3.64
9     3.88     3.65
10     3.53     3.64

(a) Find a 95% con?dence interval for µd , the meandifference in the readings using the new
method and using the standard technique (new-old).

(b) Test H0 : µd = 0 vs H1 : µd > 0 at =.05.

(c) Suppose now that we (mistakenly) interpret the paired samplesas two independent
samples. Find a 95% con?dence interval for µ1 µ2 (new-old) using either the Smith-
Satterthwaite method or the pooled method. Is your interval widerthan that in (a)?

Explanation / Answer

thanks!

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