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Math Help - determine sample size

  1. #1
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    determine sample size

    I hope someone can work out this problem for me to use as a reference for my homework. Thank you so much in advance.

    The length in centimeters if n=29 fish yielded an average length of x=16.82 (i don't know how to put the line over the x) and s^{2}=34.9. Determine the size of a new sample so that x(+/-)0.5 is an approximate 95% confidence interval for \mu.
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  2. #2
    Super Member Random Variable's Avatar
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    A 95% confidence interval for  \mu is  \bar{x} \pm z_{0.025} {\sigma \over \sqrt{n}}

     \sigma is unknown but since the sample size is fairly large, you can replace it with s

    What you want is to find a new n such that z_{0.025} {s \over \sqrt{n}} = 0.5.

    Solving for n you get  n= \frac {z_{0.025}^2 s^{2}}{0.25}
    Last edited by Random Variable; May 31st 2009 at 08:43 PM. Reason: errors
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  3. #3
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    I'm glad someone asked this question! I wasn't sure I did it correctly. It really is so simple. Since I got an answer of 536.28, it makes sense to round up to get 534. So the new sample size would be n=534.
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  4. #4
    MHF Contributor matheagle's Avatar
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    IF you did get 536.28, why would you use 534?
    and you really should round up.
    The books are weak on that point, any number above 537 would give at least that precision.
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  5. #5
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    I'm sorry, I meant to type 537. The book really did not explain that, but it maked sense. It seems to be weak in other areas as well. thank you
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  6. #6
    MHF Contributor matheagle's Avatar
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    What you're doing is setting z_{0.025} {\sigma \over \sqrt{n}}\le .5 and solving for n.

    And if you don't know \sigma, then you try to estimate it somehow.
    You may have some prior information, but you really haven't calculated s yet.
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  7. #7
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    I am so desperate to learn how to do these types of problems! To get the SD, can't I just take the square root of the variance? So since the square root of 34.9 is 5.9, sigma=5.9. Also isn't sigma the same as s?
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  8. #8
    Super Member Random Variable's Avatar
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    Quote Originally Posted by madgab View Post
    I am so desperate to learn how to do these types of problems! To get the SD, can't I just take the square root of the variance? So since the square root of 34.9 is 5.9, sigma=5.9. Also isn't sigma the same as s?
     \sigma is the standard deviation of the population

     s is the standard deviation of the sample
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  9. #9
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    i am so confused. could you work this problem through? or one similar to this? i thought they were both basically the same numbers, yet i still don't know what to do with them to complete this problem. please help me. i really think im going to need a tutor. thank you for helping
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  10. #10
    Super Member Random Variable's Avatar
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    For this problem we are assuming that they are basically the same number. But it might be the case that they're not because either our sample isn't truly representative of the entire population, or that the underlying distribution is badly skewed.
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