F(11,14)

hi,
any one tell me how to find the value of F(11,14) at 2.5%.
actually ,i know that this is find by the interpolation of the following two values:
F(10,14)=3.147 & F(12,14)=3.050
but i am confuse ,how to interpotate these two value.

 

A good question:
i tried it this way:
using F(10,14)= {X(10)/10}/{X(14)/14} where X denotes a chi-square distribution
& denoting {X(14)/14} by k, we can say that

P[{X(10)/10}/k >3.147]=0.025

& P[{X(12)/12}/k >3.050]=0.025

or P[X(10)>31.47k]=0.025
& P[X(12)>36.6k]=0.025

So to find F(11,14) at 2.5%, we need to interpolate between 31.47 and 36.6 and divide the result by 11.
ie. (36.6-31.47)/2=2.565
31.47+2.565=34.035
34.035/11=3.094

 

hi Prakhars,
I agree with your explanation ,but the value of F(11,14)=3.12

 

but i checked the value for 2.5% point of F(11,14) distribution on microsoft excel and got 3.094589791...

 

u r right ,i also got 3.0945.
But ,There is a question in the past paper of IAI( Institute of Actuaries of India). To find the 95%CI for variance ratio :
s(1)^2=.85 s(2)^2=.98
n(1)=12 & n(2)=15
( s(t)^2=sample variance & n(t)= sample size)
in indicative solution, use value of F(11,14)=3.12