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Critical region q, last part (answers given)

This question has asked me to find the critical region and is asking if I tested at the 10% significance level why the critical region would remain unaltered. It's question 8vi on this link:

http://www.mei.org.uk/files/papers/s107ju_sw8f3.pdf

The answers can be seen if you scroll down to 8vi on the markscheme, I don't understand it though. any help would be great, thanks :smile:
Original post by Magenta96
This question has asked me to find the critical region and is asking if I tested at the 10% significance level why the critical region would remain unaltered. It's question 8vi on this link:

http://www.mei.org.uk/files/papers/s107ju_sw8f3.pdf

The answers can be seen if you scroll down to 8vi on the markscheme, I don't understand it though. any help would be great, thanks :smile:


Because your distribution is discrete, your critical region can take only integer values.

Your probabilities are:
P(X=>6) = 0.1057
P(X=>7) = 0.0377

At 5%, your critical region is {7,8,9,...,17}.
But 0.10 < 0.1057, so your critical region at 10% remains the same as you can't include 6.
Reply 2
Original post by Hedgeman49
Because your distribution is discrete, your critical region can take only integer values.

Your probabilities are:
P(X=>6) = 0.1057
P(X=>7) = 0.0377

At 5%, your critical region is {7,8,9,...,17}.
But 0.10 < 0.1057, so your critical region at 10% remains the same as you can't include 6.


but why do I have to say you can't include 6? I get the bit about the critical region staying the same but not the 6 bit
Original post by Magenta96
but why do I have to say you can't include 6? I get the bit about the critical region staying the same but not the 6 bit


A 10% critical region contains all of the points that have LESS than 10% upper tail probability. So because 0.1057 > 0.10, you can't include it. If it was an 11% significance level, you would be able to include 6 in the critical region.

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