# hypothesis testing s1

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#1
why do you have to minus 1 from 0.5^3 when finding the probability of at least one day with low pollution?
question 2i) B

question:
http://pmt.physicsandmathstutor.com/...g%204%20QP.pdf

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3 years ago
#2
(Original post by esmeralda123)
why do you have to minus 1 from 0.5^3 when finding the probability of at least one day with low pollution?
question 2i) B

question:
http://pmt.physicsandmathstutor.com/...g%204%20QP.pdf

The probability that pollution is low on at least one day is equal to 1 - (the probability that pollution is NOT low on all three days).
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#3
(Original post by old_engineer)
The probability that pollution is low on at least one day is equal to 1 - (the probability that pollution is NOT low on all three days).
0.5 is the probability that it IS low on all three days so why use it?
Why not 1-0.95^3
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3 years ago
#4
(Original post by esmeralda123)
0.5 is the probability that it IS low on all three days so why use it?
Why not 1-0.95^3
did you mean 1 - 0.53 ?
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#5
(Original post by the bear)
did you mean 1 - 0.53 ?
i don't get it. why would do i that?
when it says at least 1 day, i think 1 day with low level (0.5) , 2 days with low level and three days with low level
so why would i substract 1 from 3 days with low level?
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3 years ago
#6
(Original post by esmeralda123)
i don't get it. why would do i that?
when it says at least 1 day, i think 1 day with low level (0.5) , 2 days with low level and three days with low level
so why would i substract 1 from 3 days with low level?
Well, if you want, you can calculate the probability of low pollution on exactly one day + the probability of low pollution on exactly two days + the probability of low pollution on exactly three days, but it happens to be a bit easier to do it the other way round as 1 - (the probability of low pollution on exactly no days). In this case I admit the whole thing does look a bit confusing since P(low pollution) and P(not low pollution) are both 0.5.
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3 years ago
#7
(Original post by esmeralda123)
i don't get it. why would do i that?
when it says at least 1 day, i think 1 day with low level (0.5) , 2 days with low level and three days with low level
so why would i substract 1 from 3 days with low level?
"at least one day with Low Pollution" is the opposite of "no days with Low Pollution"...
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#8
(Original post by old_engineer)
Well, if you want, you can calculate the probability of low pollution on exactly one day + the probability of low pollution on exactly two days + the probability of low pollution on exactly three days, but it happens to be a bit easier to do it the other way round as 1 - (the probability of low pollution on exactly no days). In this case I admit the whole thing does look a bit confusing since P(low pollution) and P(not low pollution) are both 0.5.
ah did you get 0.5 from 0.35+0.15

but what if there is 0.35 medium pollution for three days or 0.15 high pollution for three days?
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3 years ago
#9
(Original post by esmeralda123)
ah did you get 0.5 from 0.35+0.15

but what if there is 0.35 medium pollution for three days or 0.15 high pollution for three days?
I actually got 0.5 from 1 - 0.5 but 0.35 + 0.15 is just as good. In this context we're not worried about the exact type of "not low pollution", it just has to be "not low", and P(not low) = 0.5.
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#10
(Original post by old_engineer)
I actually got 0.5 from 1 - 0.5 but 0.35 + 0.15 is just as good. In this context we're not worried about the exact type of "not low pollution", it just has to be "not low", and P(not low) = 0.5.
also, i know this is not related but when doing hypothesis testing on two-tailed tests
do i always have to test the lower and upper tail when determining the critical region
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