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P-Value for Unknown Variance

  1. Apr 21, 2013 #1
    1. The problem statement, all variables and given/known data

    Measure of Contaminatino has a normal distribution w/ unknown mean and unknown variance. Random sample of n=40 provides sample mean = 28.30 and sample variance = 17.38

    1)Find Upper 95% Confidence Interval

    2)Test Null Hyp = 25.5 vs Alt Hyp = 28.30.... Upper Tailed

    2. Relevant equations



    3. The attempt at a solution

    1)...95% CI... therefore z(1.645) = 95%

    (xbar)+z sqrt(sigma^2 / n) = 28.30 + 1.645 sqrt(17.38 / 40) = 28.30 + 1.0843=29.38

    (0 < u < 29.38)


    2) Test Null Hyp = 25.5 vs Alt Hyp = 28.30.... Upper Tailed

    Since n = 40 we do not to use T-Tables and can just compute the P-Value from Z-Table.

    Z=(x-u)/sqrt(sigma^2/n) = (28.30 - 25.50)/sqrt(17.38 / 40) = z(4.25) = 1.00 ????

    Since it us upper tailed P-Value = 1-z(4.25) = 1-1 = 0 ?????


    Where did I go wrong... Based on my 95% CI, Shouldnt I get a little less than 95% for a value lessthan 29.38?
     
  2. jcsd
  3. Apr 22, 2013 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    The questions make no sense: 95% confidence interval of WHAT? The mean? The variance? The actual level of contamination?

    If you do want a confidence interval for the mean, you are using the wrong distribution: when you have to estimate both the mean and the variance from the data, the normal distribution does not apply. (It would apply if you knew the variance exactly and only had to estimate the mean from the data.)
     
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