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Math Help - Hypothesis Test

  1. #1
    Junior Member
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    Cool Hypothesis Test

    Pls help me to do the following

    Q)Carryout the following test using the binomial distribution where random variable X represents the number of successes.
    H0: p = 0.50; H1: p 0.05; n = 20, x = 7 and using a 10% level of significance.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Sashikala View Post
    Pls help me to do the following

    Q)Carryout the following test using the binomial distribution where random variable X represents the number of successes.
    H0: p = 0.50; H1: p 0.05; n = 20, x = 7 and using a 10% level of significance.
    Suppose that H0 holds, then calculate the probability of getting a result outside the interval np\pm 2, with p=0.5. If this probability falls below 0.1 then you reject the null hypothesis at the 10\% level of significance as the observed result is outside the given interval.

    You calculate the probability using the binomial distribution:

    P(x \in (8,12))=\sum_{i=8}^{12} b(i,0.5,20)

    where b(i,p,20) is the probability of exactly i success in n trials with probability of success on a single trial p for the binomial distribution.

    CB
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  3. #3
    Junior Member
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    Hypothesis test

    Thanks captain.
    I figured it in the following way. Pls say whether this is alright.
    Test static X has the binomial distribution which can be written as
    X ~B(20,0.5)
    This seems to be a two tailed test and since the value
    of p given for H0 is 0.5, then the distribution of the test static X will be symmetrical.
    From the table of binomial distribution
    P(x<=7)=0.1316
    So the probability for the two tailed test will be = 0.1316*2=0.2632
    Hence we cannot reject H0 for the significance level of 10%.

    Is this argument correct? Pls comment.
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