Assuming that the distribution of can weights is normal, the random variable:Originally Posted by bombo31
where is the sample mean, is the population mean,
is the sample standard deviation (the one where division is by
rather than as we need the unbiased estimator of the
population variance here), and is the sample size, has a
Student's t-distribution with degrees of freedom.
The null hypothesis is that , and then we have:
Now looking this up in an appropriate table for degrees of freedom gives:
or , and with this level of probability we would not reject the
hypothesis that .
Now we could have tried using the large sample assumption, which would then
as being normally distributed, then looking this up in a normal table we would
and so the same conclusion would be arrived at.