find the value of $Z_{\frac{\alpha}{2}}$ to construct a confidence interval with level $95\text{%}$.
The answer to this is $1.96$. But I'm having trouble seeing why. I was under the impression that you could look up $.9500$ in the normal distribution table and get the $Z$ value $2.575$, which would be the $Z_{\frac{\alpha}{2}}$. Why is it $1.96$ ?
On
Note that if you have a question asking you to find $z_{\alpha/2}$, you’re being asked to find an $\alpha$ level’s $z$-score for a two tailed test. How can we do this?
Step $1$: Note the $\alpha$ level given in the question, here as the confidence level is $95%$, we have $\alpha=0.05$.
Step $2$: Now we have $\frac12(\alpha) =0.025$. Subtracting it from $0.5$, we have the value of $0.475$.
Step $3$: Comparing the value obtained with that of the $z$- value table, we have $z=1.96$,
The $Z_{\frac{\alpha}{2}}$ that you are talking about is called the critical value in hypothesis testing in stats. You can look up the table in Mario Triola Elementary Statistics book or calculate it using the area. $\alpha = 1 - .95 = .05$. Thus $Z_{\frac{\alpha}{2}}$ is the $z$ value such that the area to the right of it is $0.025$ and this is $1.96$.