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Please help clear up Normal and t distributions for me

Discussion in 'Mathematics' started by ian60, Apr 9, 2012.

  1. ian60

    ian60 New commenter

    I understand entirely that unbiased estimators of population variance are not normally distributed.
    And so they have their own distribution, namely the t-distribution.
    So far so good.
    Now, by the CLT, shouldn't the t-distribution approach normality? So, for a sufficiently large sample size (and consequently 'degrees of freedom') we shouldn't have to consider t at all.
    If I am right in my thinking so far, how large a sample needs to be taken in order to think that the sample variances will be Normally distributed and the t-distribution becomes irrelevant?
    My current text book is not clear. I want to be able to say something along the lines of "Well, the sample size is >50, so let's just use the normal distribution"
    Thank you if you have ploughed through that, and thank you again if you can put me right.
     
  2. ian60

    ian60 New commenter

    I was too slow to edit the first paragraph.
    I understand that sample means are not normally distributed if a population SD is estimated.
     
  3. What do you call a Tea Party with more than 30 people?
    A Z Party.
     
  4. ian60

    ian60 New commenter

    Bless you charlie. I am guessing you have answered my question, albeit in a quaintly cryptic manner
     
  5. If the population is normal then the sample means are always normal even if the SD is unkown. Otherwise a sample of > 30 is standard to use the normal approximation.
     
  6. "If the population is normal then the sample means are always normal even
    if the SD is unkown. Otherwise a sample of > 30 is standard to use
    the normal approximation."

    No. If the population is normal with UNKNOWN variance, then the sample mean is technically a t-distribution. If the population is normal with KNOWN variance then the sample mean is always normaly distributed.
     
  7. Students of OCR S2
    <font size="3" face="Times New Roman">' Sould be able to; use the fact that ( the sample mean of <font size="3" face="Times New Roman">X ) </font><font size="3" face="Times New Roman">has a normal distribution if </font><font size="3" face="Times New Roman">X </font><font size="3" face="Times New Roman">has a normal distribution;'</font>
    </font>
     
  8. For students of OCR S3

    Candidates should be able to:

    use a t distribution, with the appropriate number of degrees of freedom, in the context of a small
    sample drawn from a normal population of unknown variance
     
  9. ian60

    ian60 New commenter

    Thanks to all of you who replied.
    I have decided that my uncertainty was compounded by a couple of badly worded examples in the text book I am using.
     

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