Suppose $\alpha=0.05$. How do I find the value $z_{\alpha/2}$ from a standard normal table? So $\alpha/2 = 0.025$. If I look the values $z=0.02$ and $z=0.03$ they are $0.5080$ and $0.5120$. I don't think that gets me anywhere?
If I look the table at $z=1.96$, I can see that the value is $0.9750$. Now $1-0.9750 = 0.025$ and twice that is $0.05$. (I was reading the page https://en.wikipedia.org/wiki/1.96 to get there).
I don't quite understand this. How do I do this for any $\alpha$?
I can't yet post comments asking for clarification, so here's an answer based on what I think you're asking...
Your significance level $\alpha$ is the probability of rejecting your null hypothesis when it is true. So $\alpha = 0.05$ means that you are fine with rejecting the hypothesis incorrectly 5% of the time. Wikipedia has a decent description of significance levels and types I and II errors...
I believe you must be calculating something like $\mathbb{P}(Z > z) = \alpha$, that is, the probability that your observed variable falls in the tail $\alpha$ of your distribution, and you want to find out which value of $z$ yields that.
But $\mathbb{P}(Z > z) = \alpha \Rightarrow \mathbb{P}(Z \leq z) = 1 - \alpha$. Most normal tables are constructed to give you $\mathbb{P}(Z \leq z)$ or $\mathbb{P}(0 < Z \leq z)$. So the precise way to look up the table will depend on which type of table you're using, but in most cases you will need to look up the value of $1 - \alpha$ or $1 - \alpha/2$ (again depending on the table and on the test you're doing).
