40 observed losses have been recorded in thousands of dollars and are
grouped as follows:
Interval ($000) Number of losses
(1,4/3) 16
[4/3,2) 10
[2,4) 10
[4,infinity) 4
The null hypothesis (Ho) is that the random variable X underlying the
observed losses, in thousands, has the density function
f(x) = 1/(x squared) where 1<x<infinity
Since exact value of the losses are not available, it is not possible to
compute the exact value of the Kolmogorov-Smirnov statistic used to test
Ho. However, it is possible to put bounds on the value of this statistic.
Based on the information above, determine the smallest possible value and
the largest possible value of the Kolmogorov-Smirnov statistic used to test
Ho.
A. Smallest possible value = 0.10, Largest possible value = 0.25
B. Smallest possible value = 0.10, Largest possible value = 0.40
C. Smallest possible value = 0.15, Largest possible value =
0.25
D. Smallest possible value = 0.15, Largest possible value = 0.40
E. Smallest possible value = 0.25, Largest possible value = 0.40
My attempt at the solution:
I computed F(x) = 1 - 1/x
F(1) = 0
F(4/3) = 1/4
Upper bound of (1,4/3) = 0.25
Lower bound of (1,4/3) = 0
Fn(x) = 0.40
By following the book procedure, I get K-S = 0.25 by using upper bound
and K-S = 0.40 by using lower bound.
I get 0.25 as the lowest possible answer but the manual specifies 0.15 as
the lowest possible answer. Which is correct and why ?