# Standard deviation

1. Nov 2, 2011

### gtfitzpatrick

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. Nov 2, 2011

### CompuChip

You could make your "I think" more quantitative. For example, suppose that you are given the population mean and std.dev as $\mu$ and $\sigma$, 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 $x < \mu$), assuming that $(\mu, \sigma)$ 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. Nov 2, 2011

### Ray Vickson

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