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Math Help - Determining a null and alternative hypothesis

  1. #1
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    Determining a null and alternative hypothesis

    The problem reads:

    For a sample of 20 organizations, the mean score is 5.5 with a standard deviation of 2.8. You want to use this sample to test whether or not the organizations on average have an effectiveness score greater than 5.0.

    What is your null hypothesis?

    What is your alternative hypothesis?

    (if you have time): Do the results of your sample permit you to accept the alternative hypothesis (use the appropriate value for a 95% confidence interval)
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  2. #2
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    Quote Originally Posted by endlesst0m View Post
    The problem reads:

    For a sample of 20 organizations, the mean score is 5.5 with a standard deviation of 2.8. You want to use this sample to test whether or not the organizations on average have an effectiveness score greater than 5.0.

    What is your null hypothesis?

    What is your alternative hypothesis?
    H0: average effectiveness score is greater than 5.0

    H1: average effectiveness score is less than 5.0
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  3. #3
    MHF Contributor matheagle's Avatar
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    It's not clear what the hypotheses are.

    I can see that this is a t test with 19 degrees of freedom.

    I would go with...

    H_0:\mu=5 vs H_a:\mu >5

    and the Test Stat is

     {\bar X-\mu_0\over s/\sqrt{n}} = {5.5-5\over 2.8/\sqrt{20}}

    The Rejection Region is (t_{19,\alpha }, \infty)
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  4. #4
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    I'm not sure if that's the answer I'm looking for (for that last question). I don't know what a test stat is, or the degrees of freedom. This is just asking me if "the results of the sample permit me to accept the alternative hypothesis at the 95% confidence interval.
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