Assuming that the distribution of can weights is normal, the random variable:Originally Posted bybombo31

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

justify treating:

as being normally distributed, then looking this up in a normal table we would

find that:

,

and so the same conclusion would be arrived at.