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Hypothesis testing with binomials

I was just doing a bit of last minute revision for the S2 exam tomorrow and came across this:


What does it mean when it says for the upper tail, you choose "one more than the upper of the two values where the gap occurs"? Why don't you just choose the higher value? As in, why is the critical value not 6 in that example?
Original post by olivia30
I was just doing a bit of last minute revision for the S2 exam tomorrow and came across this:


What does it mean when it says for the upper tail, you choose "one more than the upper of the two values where the gap occurs"? Why don't you just choose the higher value? As in, why is the critical value not 6 in that example?


Remember that the upper critical region is such that P(X≥c) P(X \geq c) is as close to 0.05 as possible. The key bit to all of this is the inequality.

From the tables, you read values that are P(X≤x) P(X \leq x), and the value of 1−P(X≤x)=P(X≥x+1)1 - P(X \leq x) = P(X \geq x+1). why is that? Because for a discrete distribution, if x is a number, then any number is going to either be less than/equal to or strictly greater than x in the distribution, i.e P(X≤x)+P(X>x)=1. P(X \leq x) + P( X > x) = 1. and P(X>x) is the same as P( X greater than or equal to x+1), because in a discrete distribution, if something is greater than x, an integer, then it must be greater than or equal to x+1 because there are no values inbetween (eg a binomial distriubution can't take 2.5, so if you say x>2 then x is greater than or equal to 3, and they mean the same thig.

Hence 1−P(X≤x)=P(X≥x+1)1 - P(X \leq x) = P(X \geq x+1) so the P( X less than or equal to x) value you read off the table, which is as close to 0.95 as possible, you have to add 1 more to that x value find the c value such that P(X greater than or equal to c) is as close to 0.05 as possible.
(edited 7 years ago)
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olivia30
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Original post by SeanFM
x


Thank you so much, you are amazing! :h:
Original post by olivia30
Thank you so much, you are amazing! :h:




No worries :tongue: sorry that the latex just doesn't work :hide: but hopefully you get it.
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olivia30
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Original post by SeanFM
No worries :tongue: sorry that the latex just doesn't work :hide: but hopefully you get it.


My latex never works either :lol: it's fine to read though, thanks again :smile:

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