In my homework, I was asked to find the standard error of mean for 2 cases and then do the 5% and 1% test for both of them.
I know how to work out stand error of mean, but I don't know how to use it to find the hypothesis testing, can someone help me please?
If you are being asked to use the standard error for a hypothesis test, then they are implicitly assuming that the mean is approximately normally distributed. Therefore, you will use the standard error to get your usual Z-statistic: $Z=\frac{\bar X-\mu}{se}$, which will have, approximately, a $\mathcal{N}(0,1)$ distribution. Now, you just need use the usual cutoofs for the z-test for your given significance level.