If we want to evaluate P(chi square with n degrees of freedom>=k)=0.05
should I say k=chi square(n,0.05) or k=chi square (n, 1-0.05)?
I am not sure since I don't know if >= or <= makes a difference in chi square distribution as it does in normal distribution (which is symmetric), but chi square is not!
Any help would be appreciated, thank you
Depends on the table/technology you are using.
To find a critical value, let's say df=15
CHIINV(0.95,15) = 7.26 (left tail)
CHIINV(0.05,15) = 25.00 (right tail)
Draw a picture of the curve with these values on it, does it help?
Basically I have the following (which is a part from a problem I solved):
Under Ho (null hypothesis)
P(Sum from i=1 to 50 of Xi >= k) = P(Sum from i=1 to 50 of 4*Xi >=4k) = P(chi square with 200 df >= 4k) since I had deduced in the problem that the sum follows that distribution.
But at the same time P(Sum from i=1 to 50 of Xi >=k) = 0.05 (0.05 is the power of my test)
The problem had to do with most powerful test and region. The thing is that P(Sum from i=1 to 50 of Xi >=k) = 0.05 if and only if 4k = chi square with 200 df but looking at 0.05 or 0.95? This was my question!
If I had P(Sum from i=1 to 50 of Xi <= k) = 0.05 it would be a different case? So this is my question, if my sum >=k or my sum <=k would change the value of chi square with 200 df I should look in my tables.
I hope I got clear this time with my question
In my problem I have the sum >=k, not <=k!