Question

state the zcrit for the following situation: alpha = 5% two tails

Explanation:

Step1: Determine significance level for each tail

For a two - tailed test with \(\alpha = 5\%=0.05\), the significance level for each tail is \(\frac{\alpha}{2}=\frac{0.05}{2} = 0.025\).

Step2: Find the z - score corresponding to the area

We need to find the \(z\) - score such that the area to the right of \(z\) (in the upper tail) is \(0.025\). This means the area to the left of \(z\) is \(1 - 0.025=0.975\).
Looking up the value in the standard normal distribution table (or using a calculator with a normal - distribution function), the \(z\) - score corresponding to an area of \(0.975\) to the left is approximately \(1.96\). Since it is a two - tailed test, the critical \(z\) - values are \(\pm1.96\).

Answer:

The critical \(z\) - values (\(Z_{crit}\)) for a two - tailed test with \(\alpha = 5\%\) are \(\pm1.96\)