Problems 413
that each animal has a random threshold and will become ill if the dosage level exceeds
that threshold. The exponential distribution has sometimes been used as the threshold
distribution. For instance, a model considered in Freedman and Zeisel (“From Mouse to
Man: The Quantitative Assessment of Cancer Risks,”Statistical Science, 1988, 3 , 1, 3–56)
supposes that a mouse exposed toxunits of DDT (measured in ppm) will contract cancer
of the liver with probability
p(x)= 1 −e−ax, x> 0
Becauseofthelackofmemoryoftheexponentialdistribution, thisisequivalenttoassuming
that if the mouse who is still healthy after receiving a (partial) dosage of levelxis as good
as it was before receiving any dosage.
It was reported in Freedman and Zeisel that 84 of 111 mice exposed to DDT at a level
of 250 ppm developed cancer. Therefore,αcan be estimated from
1 −e−^250 αˆ=
84
111
or
αˆ=−
log(27/111)
250
=.005655 ■
Problems.........................................................
- The following data relatex, the moisture of a wet mix of a certain product, toY,
the density of the finished product.
xi Yi
5 7.4
6 9.3
7 10.6
10 15.4
12 18.1
15 22.2
18 24.1
20 24.8
(a) Draw a scatter diagram.
(b) Fit a linear curve to the data.