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    sample percentage contained within symmetric limits




    Hi!
    Thank you in advance for assisting with my question.
    I am working on a probability question and am able to answer almost all of it except one final part. The answer reads: " The probability is 95% that the sample percentage will be contained within 6.94% symmetrically around the population mean." I can not figure out how the 6.94% was obtained. I realize that .0694 equals the Z value -1.48, but that doesn't help me.

    The full question is "The probability is 95% that the sample percentage will be contained within what symmetrical limits of the population percentage."
    Here is my work:
    n = 200,
    π = .5
    p = .5

    1-.95 =.5
    .5/2= .0250
    Z value of .0250 = -1.96
    Z value of .9750 (.95 + .0250 =.9750) is +1.96

    -1.96 <Z <+1.96

    A = .5 + (1.96 * .0354) =.5694
    B = .5 (1.96* .0354) =.4306

    I searched in my textbook, other statistic books and online, but still can not figure this out.
    Any help would be greatly appreciated.
    Thanks,

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    Re: sample percentage contained within symmetric limits

    Quote Originally Posted by ealeql View Post
    Hi!
    Thank you in advance for assisting with my question.
    I am working on a probability question and am able to answer almost all of it except one final part. The answer reads: " The probability is 95% that the sample percentage will be contained within 6.94% symmetrically around the population mean." I can not figure out how the 6.94% was obtained. I realize that .0694 equals the Z value -1.48, but that doesn't help me.

    The full question is "The probability is 95% that the sample percentage will be contained within what symmetrical limits of the population percentage."
    Here is my work:
    n = 200,
    π = .5
    p = .5

    1-.95 =.5
    .5/2= .0250
    Z value of .0250 = -1.96
    Z value of .9750 (.95 + .0250 =.9750) is +1.96

    -1.96 <Z <+1.96

    A = .5 + (1.96 * .0354) =.5694
    B = .5 – (1.96* .0354) =.4306

    I searched in my textbook, other statistic books and online, but still can not figure this out.
    Any help would be greatly appreciated.
    Thanks,
    I suspect that what your textbook is getting at is that using the difference between the upper and lower limits of your interval we can obtain:

    (.5694 - .4306) / 2 = ( .1388) /2 = .0694 or 6.94%.

    Is that correct--- or am I right?

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    Re: sample percentage contained within symmetric limits

    Quote Originally Posted by Dragan View Post
    Is that correct--- or am I right?
    Both. I like your style.

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    Re: sample percentage contained within symmetric limits


    Thank you very much of answering this question. I really appreciate it.

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