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Math Help - Hypothesis Testing

  1. #1
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    Hypothesis Testing

    "A manufacturer claims that 20% of the public preferred her product. A sample of 100 persons is taken to check her claim. It is found that 8 of these 100 persons preferred her product. Using the 0.05 level of significance test her claim (perform a two-sided test), and Find the p-value and explain what it means."

    I think I understand what to do, but I don't get how to find the standard deviation for this sample.. After that, I know I'm supposed to create a Z-score, and see if it is in the rejection region, but without the SD, I can't get anywhere. I tried to assume this was a binomial distribution, and got SD = sqrt(npq), but the answer comes to accepting the H0 hypothesis, which is ridiculous.

    Help! Thanks in advance!
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  2. #2
    Grand Panjandrum
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    Re: Hypothesis Testing

    Quote Originally Posted by limddavid View Post
    "A manufacturer claims that 20% of the public preferred her product. A sample of 100 persons is taken to check her claim. It is found that 8 of these 100 persons preferred her product. Using the 0.05 level of significance test her claim (perform a two-sided test), and Find the p-value and explain what it means."

    I think I understand what to do, but I don't get how to find the standard deviation for this sample.. After that, I know I'm supposed to create a Z-score, and see if it is in the rejection region, but without the SD, I can't get anywhere. I tried to assume this was a binomial distribution, and got SD = sqrt(npq), but the answer comes to accepting the H0 hypothesis, which is ridiculous.

    Help! Thanks in advance!
    Under the null hypothesis the number who prefer the product in a sample of 100 has a binomial distribution B(100,0.2).

    CB
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  3. #3
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    Re: Hypothesis Testing

    So, simulating the actual test as a binomial distribution b(100,0.08), the expected value is 8. Also, under the null hypothesis, the expectation is 20, and standard deviation is 4. So, the Z score would be (8-20)/(4/sqrt(100))? That gives me a P(Z<-30), which would clearly reject the null hypothesis.
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  4. #4
    MHF Contributor matheagle's Avatar
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    Re: Hypothesis Testing

    I used the normal approximation and got a test stat of -3, not 30.
    So the approximate p-value is

    2P(Z<-3)
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  5. #5
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    Re: Hypothesis Testing

    got it. I guess since i'm not working with the mean, I dont need to include the sqrt(100) at the bottom. thank you!
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