S2 question, please answer asap

Hi all

The question goes like this:
A single observation x is to be taken from a Poison distribution with paramater A, This observation is to be used to test H0:A=7 against H1:A =/ 7.
Using a 5% sig. level, find the CR for this test assuming that the pro. of rejecting in either tail is as close as possible to 2.5%

What I have got is:
P(X<=1)=0.0073 and P(X>=14)=1-0.9872=0.0128
CR: X<=1 or X>=14

But what the mark scheme gives is:
P(X<=2)=0.0296
P(X>=13)=1-0.9730=0.0270
CR X<=2 or X>=13

I see they try to make Critical Level closer to 5% overall, but in the exam how do I know where to change? Or Would I get all marks with my present answer? Please let me know asap, thanks.

Reply 1

m:)ckel

If they say 'as close as possible' (as above) then you have to take values that are as close as the sig level as possible, regardless of whether they're over the level.

If they simply ask for the critical regions, then you would have to do as you did, and take the values of X giving just less than the sig level.