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Math Help - Hypothesis Testing and Finding P-Value

  1. #1
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    Hypothesis Testing and Finding P-Value

    Although 85% of the general public is right-handed, a survey of 300 chief executive officers of large corporations found that 96% were right-handed.

    a) Is this difference in percentages statistically significant? Test using α = 0.01.
    b) Find the p-value for the test and explain what it means.

    Attempt At Solution

    a) The rejection region is {z > 2.33}.

    Using the test:

    z = (p - p0)/(sqrt(p0*(1-p0)/n), where p0 = .85, p = .96, and n = 300

    I got z = 5.34. Since 5.34 > 2.33, this lies in the rejection region and thus, the difference is significant.

    b) p-value = P(Z > 5.34) = 0.000000287

    Since this value is so small, it is evident that the null hypothesis should be rejected.

    Is this correct?
    Last edited by My Little Pony; March 16th 2011 at 09:29 AM.
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  2. #2
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    It isn't clear to me that the test should be one-sided, but other than that it looks fine.
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  3. #3
    MHF Contributor matheagle's Avatar
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    agreed
    it should be clear what you're trying to prove
    when I see the word difference, I think of a two-sided test
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