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S2 - Finding a critical region

im just about there, but i always seem to be one off of what the answer should be. for example:

The probability of Brand A lotion curing a particular skin complaint it 0.35. Brand B is said to improve the cure rate. Brand B was tested on 20 people, and 10 people were cured of the problem. Show Brand B isnt significant at 0.05, and how many people out of 20 would be needed to be cured so the results are significant to 0.05?


This means

H0: p=0.35
H1: p>0.35

X~B(20,0.35)


P(X≥10) = 1-P(X≤9) = 1-0.8782 = 0.1218. >0.05 therefore not significant.


P(X≥c) ≤ 0.05

1-P(X≤c-1) ≤ 0.05

P(X≤c-1) ≥ 0.95

now from the table,
P(X=10) = 0.9468
P(X=11) = 0.9804

therefore c-1=11 and c=12


but...the answer says its 11, not 12. what have i done wrong?
Reply 1
Avatar for alex_hk90
alex_hk90
19
I can't find anything wrong with your working.
Where was the question from?
The only thing I can think of is that they might have rounded 0.9468 to 0.95, but it's very unlikely.
Reply 2
Avatar for Method
Method
12
I can't see anything wrong with your working either. Where did you get this question from, is from the book or an exam paper? :smile:
Reply 3
Avatar for rufnek2k6
rufnek2k6
12
nope, nothing wrong with your answer, think the book is wrong on this one, i hate it when this happens cuz then you keep thinking youve made the mistake and keep goin over an ovr tryin to find something that isnt there.
Reply 4
Avatar for danny_g
danny_g
OP
it was from my Heinemann S2 textbook. i seem to get them wrong in past papers by about 1 like i said, so i went back to my textbook and started doing lots of the same type of question.

im gonna keep practicing them anyway, but its good news that i did it right and it is the answer that is wrong. :smile:

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