Standard deviation

  • #1

Homework Statement



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?

Homework Equations





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?
 

Answers and Replies

  • #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.
 
  • #3
Ray Vickson
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Homework Statement



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?

Homework Equations





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?
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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