I am working on the following problem.
A state wildlife service wants to estimate the mean number of days that
each licensed hunter actually hunts during a given season, with a bound
on the error of estimation equal to 2 hunting days. If data collected .
in earlier surveys have shown σ to be approximately equal to 10, how
many hunters must be included in the survey?
My understanding is that $\mu$ is being approximated, $\sigma=10$ and the margin of error $m =2$. I do not think the confidence level is explicit in this problem and yet the solution of this problem states that the sample must be $n=100$.
My understanding is that $${z_{\frac{\alpha}{2}}{\sigma \over \sqrt n}}=m$$
So without knowing the critical value or the confidence level we cannot solve for $n$.
The solution for some reason chose the critical value to be $2$. Is this a conventional thing in statistics or am I missing something?