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Math Help - Confidence in temperature

  1. #1
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    Post Confidence in temperature

    Using column temp, we can compute the sample mean
    temp = 19:74, sample size = 150 and the sample standard deviation stemp = 6:035.
    (a) Construct a 91% confidence interval for the population mean of

    temp.
    (b) If we want ensure the error margin of the 91% confidence interval to be less than 0.5, what sample size should we take (assuming that the sample standard deviation is a good estimate of the population standard deviation)?
    is the error margin of the 91% confidence interval different to the error margin of x-bar? (s\sqrt{n}), how would you calc the approx sample size?
    2. Construct a 95% confidence interval for the proportion of forest fires that occur when the temperature is greater than 25 degrees celsius.
    I found the values in the data set >25 degrees which made n=21, x-bar=28.533 and s=2.467, then I just did the normal confidence interval formula to work it out. Did I go about that the right way?

    Cheers,

    Jay
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    Last edited by JMan69; May 25th 2011 at 05:36 AM. Reason: answered question 2 and deleted answers
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  2. #2
    MHF Contributor matheagle's Avatar
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    well, there is a slight distinction.....
    IF the data is normal then this is a t with 149 df, which is darn close to a N(0,1)
    IF the data is not from a normal distribution then you can use the CLT and get an approximate CI using the Z.

    \bar X \pm t_{n-1,\alpha/2}S/\sqrt{n}

    or \bar X \pm Z_{\alpha/2}S/\sqrt{n}

    Next use Z_{\alpha/2}S/\sqrt{n}\le .5 and solve for the smallest n that works.
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