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Math Help - population proportion

  1. #1
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    population proportion

    I get z= 1.40 and so the confidence 91.92% but the book says 84.14%.

    Can you check it out please?

    Of a random sample of 198 students 98 rated the case of resume inflation as unethical. Based on this info, a statistician computed for the population proportion a confidence interval extending from 0.445 to 0.545. What's the confidence level of this interval?


    Thank you for all your help.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by 0123 View Post
    I get z= 1.40 and so the confidence 91.92% but the book says 84.14%.

    Can you check it out please?

    Of a random sample of 198 students 98 rated the case of resume inflation as unethical. Based on this info, a statistician computed for the population proportion a confidence interval extending from 0.445 to 0.545. What's the confidence level of this interval?


    Thank you for all your help.
    If I said 2-sided rather than 1-sided would that mean anything to you?

    RonL
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    Quote Originally Posted by CaptainBlack View Post
    If I said 2-sided rather than 1-sided would that mean anything to you?

    RonL
    I think that one side is when you have the gaussian and you "color" everything below the curve up to a certain point; two sided when you color the curve under an interval. Here using both UCL and LCL I get z=1.40. I though that to any level of z there corrisponds one and only one level of confidence(which I can find as F(x) in the table). Might you help me understand? thank you so much.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by 0123 View Post
    I think that one side is when you have the gaussian and you "color" everything below the curve up to a certain point; two sided when you color the curve under an interval. Here using both UCL and LCL I get z=1.40. I though that to any level of z there corrisponds one and only one level of confidence(which I can find as F(x) in the table). Might you help me understand? thank you so much.
    This is a symmetric confidence interval thet extends from z= -1.4 to +1.4.

    The table gives the probability p(z<1.4) ~= 91.92.

    We have p(-1.4<z<1.4) = p(z<1.4) - p(z<-1.4) by symmetry this gives:

    p(-1.4<z<1.4) = p(z<1.4) - p(z<-1.4) = 1 - 2[1-p(z<1.4)]


    RonL
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    Quote Originally Posted by CaptainBlack View Post
    This is a symmetric confidence interval thet extends from z= -1.4 to +1.4.

    The table gives the probability p(z<1.4) ~= 91.92.

    We have p(-1.4<z<1.4) = p(z<1.4) - p(z<-1.4) by symmetry this gives:

    p(-1.4<z<1.4) = p(z<1.4) - p(z<-1.4) = 1 - 2[1-p(z<1.4)]


    RonL
    Yes, I came to understand what you meant. I did Okay 91.92 colors up to that point but we want the interval that leaves the same both at left and at right. How much is left right? Let's see= 100-91.92= 8.08
    So we take off 8.08 from the colored part and we get 91.92-8.08= 83.84.

    But it is not 84.14, as in the book. Is it just approximation right? I can be okay with this result? Sorry for being so annoying Thank you so much.
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  6. #6
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    Quote Originally Posted by 0123 View Post
    Yes, I came to understand what you meant. I did Okay 91.92 colors up to that point but we want the interval that leaves the same both at left and at right. How much is left right? Let's see= 100-91.92= 8.08
    So we take off 8.08 from the colored part and we get 91.92-8.08= 83.84.

    But it is not 84.14, as in the book. Is it just approximation right? I can be okay with this result? Sorry for being so annoying Thank you so much.
    The interval in question is actually closer to z=-1.41 to z=1.41 rather than 1.4.

    RonL
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