Question

Assume that random variable x^2 has a chi-squared distribution with v degree of freedom. Find the value of “A” for the following cases

1) P(X^2 <=A) =.95 when v = 6

2) P(X^2>=A) =.01 when v = 21

3) P(A <= X^2 <= 23.21)= .015 when v = 10.

Answer 1

You can use the excel function =CHIINV( probability , d.f ) to find the chi square value A.

probability = area greater than( or to the right of ) chi square value A , d.f = degrees of freedom.

1) P(X^2 <=A) =.95 when v = 6

We have to find chi square value A such that area below ( or left to ) A is 0.95

So first we need to find area to the right of A = 1 - area to the left

= 1 - 0.95 = 0.05

So probability = 0.05 , d.f = 6

So A = 12.59

2) P(X^2>=A) =.01 when v = 21

We have to find chi square value A such that area greater than ( or right to ) A is 0.01

Therefire probability = 0.01 , d.f = 21

So A = 38.93

3) P(A <= X^2 <= 23.21)= .015 when v = 10.

We are asked to find A such that area between A and 23.21 is 0.015

So first we need to find area greater than 23.21 using the excel function =CHIDIST( x , d.f )

Here x = 23.21 and d.f = 10

So area to the right of 23.21 is 0.009997

So the total area to the right of A = Area to the right of 23.21 + area between A and 23.21

= 0.00997 + 0.015

= 0.0249997

So to find the A we have to use function CHIINV( probability , d.f )

So the answer A = 20.48