Alevel maths help

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godemperor
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#1
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#1
A discrete random variable x has a Binomial distribution B(30, p). A single observation is used to test H0 : p = 0.3 against H1 : p >0.3

X~B(30,0.3), using 1% significant level find the critical region and state the probability of rejection.

not sure what the answer is but I got X ≤ 3 and probability of failure is 0.0093.
Can some one tell me if im right or how i can get the right answer
Last edited by RIF A; 1 year ago
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old_engineer
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#2
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#2
(Original post by RIF A)
A discrete random variable x has a Binomial distribution B(30, p). A single observation is used to test H0 : p = 0.3 against H1 : p >0.3

X~B(30,0.3), using 1% significant level find the critical region and state the probability of rejection.

not sure what the answer is but I got X ≤ 3 and probability of failure is 0.0093.
Can some one tell me if im right or how i can get the right answer
It looks to me as though you've carried out a correct hypothesis test for H1: p < 0.3 rather than p > 0.3
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turkeydinosaur16
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#3
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(Original post by RIF A)
A discrete random variable x has a Binomial distribution B(30, p). A single observation is used to test H0 : p = 0.3 against H1 : p >0.3

X~B(30,0.3), using 1% significant level find the critical region and state the probability of rejection.

not sure what the answer is but I got X ≤ 3 and probability of failure is 0.0093.
Can some one tell me if im right or how i can get the right answer
I think your method is correct but I think you've looked at the wrong tail of the test. H1 says p>0.3 so you're looking for the likelihood of more of 'x' being selected than expected (i.e. in a perfect world you'd expect 0.3*30 = 9 successful outcomes but if H1 is true, there'd be more successful outcomes so the value would be greater than 9). You therefore need to look at the cumulative probability in the table that exceeds 0.99 e.g. where the outcomes after this point collectively add to 0.01.

Using the statistics table, I got p(X ≤ 15) = 0.9936

The last step is to convert this to show which value and above result in a less than 1% likelihood. Let me know if you need any help on this
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godemperor
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#4
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(Original post by turkeydinosaur16)
I think your method is correct but I think you've looked at the wrong tail of the test. H1 says p>0.3 so you're looking for the likelihood of more of 'x' being selected than expected (i.e. in a perfect world you'd expect 0.3*30 = 9 successful outcomes but if H1 is true, there'd be more successful outcomes so the value would be greater than 9). You therefore need to look at the cumulative probability in the table that exceeds 0.99 e.g. where the outcomes after this point collectively add to 0.01.

Using the statistics table, I got p(X ≤ 15) = 0.9936

The last step is to convert this to show which value and above result in a less than 1% likelihood. Let me know if you need any help on this
thanks
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