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Math Help - What is "unusual"?

  1. #1
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    What is "unusual"?

    When we choose whether a value of the mean (x bar) is "unusually" far from the mean (mu) is a matter of choosing whether:

    (x bar - mu)/(sigma/root(n)) is "unusually" far from zero.

    The concern is, what is "unusual"?

    It it were defined as "occuring on less than 5 % of occassions"
    • what range of values of (x bar - mu)/(sigma/root(n)) would be regarded as unusually far from zero?

    • what would this range be if we replace 5% by 1%?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by nacknack View Post
    When we choose whether a value of the mean (x bar) is "unusually" far from the mean (mu) is a matter of choosing whether:

    (x bar - mu)/(sigma/root(n)) is "unusually" far from zero.

    The concern is, what is "unusual"?







    It it were defined as "occuring on less than 5 % of occassions"
    • what range of values of (x bar - mu)/(sigma/root(n)) would be regarded as unusually far from zero?

    • what would this range be if we replace 5% by 1%?
    Because you are talking about a sample mean and I am ging to assume a large sample:

    z=\frac{\overline{x}-\mu}{(\sigma/\sqrt{n})}

    has (approximatly) a standard normal distribution. Now look up the critical value z_{crit} for 5% and 1% (that is z_{crit}=P^{-1}(0.95) and z_{crit}=P^{-1}(0.99) where P is the cumulative distribution function for the standard normal distribution), and then any value of z greater than this is "unusual"

    CB
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