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S1 hypothesis testing question

A random variable has distribution B(10,p). A single observation is used to test H0: p=0.22 against H1: p is not equal to 0.22.

a) Using a 1% level of significance, find the critical region of this test. The probability in each tail should be as close as possible to 0.005.

I got two solutions but the answer given only gives the region where X is greater than 7. Why is there no solution in the lower tail?? I get there's no 'x' value where the P(B<=x)<0.005 but if the question states the probability should be as close to 0.005, then why is 0 not an answer?
Original post by dont know it
A random variable has distribution B(10,p). A single observation is used to test H0: p=0.22 against H1: p is not equal to 0.22.

a) Using a 1% level of significance, find the critical region of this test. The probability in each tail should be as close as possible to 0.005.

I got two solutions but the answer given only gives the region where X is greater than 7. Why is there no solution in the lower tail?? I get there's no 'x' value where the P(B<=x)<0.005 but if the question states the probability should be as close to 0.005, then why is 0 not an answer?


P(X<=0)=0.08336
P(X< 0) = 0

Which is closer to 0.005? The second one - so there is no lower tail, since you can't get a value of X less than zero.
Original post by ghostwalker
P(X<=0)=0.08336
P(X< 0) = 0

Which is closer to 0.005? The second one - so there is no lower tail, since you can't get a value of X less than zero.

Hmm I'm kinda confused. Not that I don't understand what you just said, but I always thought the critical region had to be x<= something or x>= something. I didn't know this was possible. If I found a critical region to be x<=6, would it be right if I said x<7 which would be the same thing since the variable is discrete?
Original post by dont know it
Hmm I'm kinda confused. Not that I don't understand what you just said, but I always thought the critical region had to be x<= something or x>= something. I didn't know this was possible. If I found a critical region to be x<=6, would it be right if I said x<7 which would be the same thing since the variable is discrete?


For a r.v. taking only integer values, then yes, they define the same region.
Original post by ghostwalker
For a r.v. taking only integer values, then yes, they define the same region.

Ok thank you.

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