chi-square distribution

How do I use the percentage point table for chi-square? Please explain with reference to Example 4.1 or any other example.

 

Example 4.1
Given that \(X\backsim(\chi_5^2)\), then find that \(P(X<6.5)\).
Therefore \(P(X>6.5)=1-P(X\leq6.5)=1-(P(\chi_5^2)\leq6.5)=1-0.7394=0.2606\)
We have to use the TABLE's Page No.165 to get the value of \((P(\chi_5^2)\leq6.5)\)

 

Thanks for the reply but I understood how to use the tables on probabilities on chi-square.

but it is also written in the end of the example that we could also use the tables on page 168-169.
how do I use those tables?

 

In percentage point table we start with a probability and then find a corresponding value for it, whereas its the opposite in the probability tables.

For using percentage point table for this ques P(X > 6.5),
see pg 169 and in the 5 degree of freedom row, look for value 6.5

It is between 6.064 (30%) and 7.289 (20%).
So we've to interpolate between these two values. You'll get approximately the same answer.

 

Hope you know the interpolation method.
Table's Page No.164-166 the data of x value given, and on the Page no.168-169 the Probability value is given.
We got \(P(X<11.8)\)
From the Table's Page no.169 we could revealed that Probability of Chi-Square with 5 degrees of freedom is within 11.07 and 12.83.
It does mean that we need to get the interpolation value between \(P(X<11.07)=0.05\) and \(P(X<12.83)=0.025\)

 

Thank you so much-asmkdas and suraj.