Question

two tails
α = 0.20 → each tail 0.10
zcrit = ±1.2816

Explanation:

Step1: Understand two - tailed test and α

For a two - tailed test, the significance level \(\alpha = 0.20\) is split equally between the two tails. So the area in each tail is \(\frac{\alpha}{2}=\frac{0.20}{2} = 0.10\).

Step2: Find the z - critical value

We need to find the \(z\) - value such that the area to the right of \(z_{crit}\) (in the upper tail) is \(0.10\) and the area to the left of \(-z_{crit}\) (in the lower tail) is \(0.10\). Looking at the standard normal distribution table (or using a calculator with a normal - distribution function), the \(z\) - value corresponding to an area of \(0.10\) in the upper tail (or \(0.90\) in the lower tail) is approximately \(1.2816\). Since it is a two - tailed test, the critical values are \(\pm1.2816\).

Answer:

The critical \(z\) - values for a two - tailed test with \(\alpha = 0.20\) are \(\boldsymbol{\pm1.2816}\)