Question

Determine the level of the confidence given the confidence coefficient z(a/2) for the following situation: z(a/2) = 1.96

Answer 1

The shaded areas add up to \(\alpha\), so that each shaded area individually amounts to \(\alpha/2\). The probability that a test statistic \(Z\) falls to the right of the positive critical coefficient is given as
\[P(Z>Z_{\alpha/2})=\frac{\alpha}{2}\]
where \((1-\alpha)\times100\%\) is the confidence level.

You can use a z-table (such as this one http://www.rochester.edu/college/psc/clarke/201/ztable2.jpg ) to determine the value \(\dfrac{\alpha}{2}\) by solving,
\[P(Z>1.96)=\frac{\alpha}{2}\]