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Math Help - problem understanding one thing in hypothesis testing of discrete variables

  1. #1
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    Unhappy problem understanding one thing in hypothesis testing of discrete variables

    hi,

    Ok so I understand the problems and what I have to do. This chapter is straight after hypothesis testing of continuous variables.

    I just dont understand ONE thing..

    Problem 1 :
    One evening on a estate playground 12 boys and 6 girls were playing. Assuming these were a random sample of all children living in the estate, test, and the 10% significance level, whether there are equal numbers of Boys and girls on the estate.
    So the solution to this was X ~ B(18, 0.5) (X follows a binomial distribution)
    find P(X >= 12) which is 11.9% since its a two tail test 11.9 > (10/2) % so the boys and girls are equal.

    Problem 2
    A car dealer claims atleast 95% of his customers are satisfied. In A random sample of 25 of them 22 said they were satisfied. Test at 5% sig level that the data supports his claim.
    So here X ~ B(25, 0.95) but when I calculated P(X>=22) i was wrong, apparently I had to calculate P(X<= 22)

    Why P(X<=22) how do I know when I have to look for greater than ??

    I'm very sorry if this is a stupid question but I am learning on my own!
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  2. #2
    MHF Contributor matheagle's Avatar
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    These are the p-values, the probability of being worse off than the data, assuming the null hypothesis is correct.
    In the first case, you assume under the null that it's equally likely to see a male or female out of 18 children, so p=.5 under the null.
    You observe 12 males, hence the p-value is 2P(X\ge 12) where n=18 and p=.5
    and you double it since this is a two sided test.

    H_o: p=.5 vs. H_a: p\ne .5

    You then compare the p-vale to your alpha in order to make a decision.

    In the second one, I'D put the thing I want to prove in the althernative hypothesis.

    Hence my alternative is H_a: p\ge .95

    The null can either be H_o: p<.95 or for simplicity H_o: p=.95
    Both are treated the same.
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  3. #3
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    Sorry I didnt reply sooner. Yea I understood after a while! =P Also I realized I have to look for a probability that is usually small, if I get the direction wrong the probability is opposite.
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