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Math Help - Statistics: Area equal to p-value on standard curve

  1. #1
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    Statistics: Area equal to p-value on standard curve

    I'm currently reviewing for a statistics final, and have been using the practice final supplied in class to do so. I understand the material, the problem lies in a difference between the answer I got (which was, by the way, the same as the one reached by a math tutor I asked) and the one the teacher supplied. In case I missed some important detail, I'll supply everything we were provided.

    A sample of n=200 college students is asked if they believe in extraterrestrial life and 120 of these students say that they do. The data are used to test:
    Ho: p=0.5 vs Ha: P>0.5
    Where p is the population proportion of college students who say they believe in extraterrestrial life. The following information is provided:

    X=120
    N=200
    Sample p=0.60000
    95% Confidence Interval=(0.532105,0.667895)
    Z-value=2.83
    p-value=0.002

    What is the correct description of the area that equals the p-value for this problem?
    a.)
    The area to the right of 0.60 under a standard normal curve
    b.) The area to the right of 2.83 under a standard normal curve
    c.) The area to the right of -2.83 under the normal standard curve.
    d.) The area between 0.532105 and 0.667895 under a normal standard curve.

    The answer I got was b, with a and d being eliminated at possible answers because the numbers they're based on doesn't concern the Z-value, on which the area in question is based. Now, to my understanding, it would be the area to the right of 2.83, as the p-value is greater than 0.5, rather than being less than. The teacher, however, supplied the answer as being c, and I want to clarify which it is, rather than going into the exam unprepared. Any help, explanation, even agreement is greatly appreciated.

    Thanks,

    Tim
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  2. #2
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    Quote Originally Posted by Lucky Color Seven View Post
    I'm currently reviewing for a statistics final, and have been using the practice final supplied in class to do so. I understand the material, the problem lies in a difference between the answer I got (which was, by the way, the same as the one reached by a math tutor I asked) and the one the teacher supplied. In case I missed some important detail, I'll supply everything we were provided.

    A sample of n=200 college students is asked if they believe in extraterrestrial life and 120 of these students say that they do. The data are used to test:
    Ho: p=0.5 vs Ha: P>0.5

    Where p is the population proportion of college students who say they believe in extraterrestrial life. The following information is provided:



    X=120


    N=200


    Sample p=0.60000


    95% Confidence Interval=(0.532105,0.667895)


    Z-value=2.83


    p-value=0.002



    What is the correct description of the area that equals the p-value for this problem?


    a.) The area to the right of 0.60 under a standard normal curve


    b.) The area to the right of 2.83 under a standard normal curve


    c.) The area to the right of -2.83 under the normal standard curve.


    d.) The area between 0.532105 and 0.667895 under a normal standard curve.



    The answer I got was b, with a and d being eliminated at possible answers because the numbers they're based on doesn't concern the Z-value, on which the area in question is based. Now, to my understanding, it would be the area to the right of 2.83, as the p-value is greater than 0.5, rather than being less than. The teacher, however, supplied the answer as being c, and I want to clarify which it is, rather than going into the exam unprepared. Any help, explanation, even agreement is greatly appreciated.



    Thanks,



    Tim

    The correct answer is b.)

    Note also that the p-value is given to be 0.002 and in fact Pr(Z > 2.83) = 0.002.
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  3. #3
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    Much appreciated, Mr. Fantastic. I've been stressing about this, and it's good to have my answer confirmed.
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