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Standard deviation

  1. Nov 2, 2011 #1
    1. The problem statement, all variables and given/known data

    i'm given the population mean and standard deviation. A new batch comes in and given a random sample. the question asks do i believe the new batch has a different mean from the overall average?

    2. Relevant equations



    3. The attempt at a solution

    so i got the mean and standard deviation of the new batch. They are much different from the population mean and standard deviation. But i don't believe they are different the sample standard deviation is less than the population standard deviation, am i right in my thinking?
     
  2. jcsd
  3. Nov 2, 2011 #2

    CompuChip

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    You could make your "I think" more quantitative. For example, suppose that you are given the population mean and std.dev as [itex]\mu[/itex] and [itex]\sigma[/itex], and you measure a mean x on the random sample.

    Now you can calculate the probability that if you were to do the experiment you just did, you would get a mean of at least x (or at most x, if [itex]x < \mu[/itex]), assuming that [itex](\mu, \sigma)[/itex] are the actual distribution.
    If that gives you a very small probability (like 0.0002%) then that means that your assumption is probably incorrect - given that you've just done the experiment and still found that unprobable outcome.
     
  4. Nov 2, 2011 #3

    Ray Vickson

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    Was this last thing supposed to be a sentence in English? It isn't.

    Google "t-test" and/or "F-test", although these require normally-distributed data.

    RGV
     
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