Question

bonpoc 8
state the zcrit for the following situation:
alpha = 20%
two tails

Explanation:

Step1: Determine the significance level for each tail

Given a two - tailed test with $\alpha = 20\%=0.20$, we divide the significance level by 2 to get the significance level for each tail. So, $\frac{\alpha}{2}=\frac{0.20}{2} = 0.10$.

Step2: Find the z - score corresponding to the area

We want to find the z - score such that the area to the right of it (in one tail) is 0.10. The area to the left of the z - score will be $1 - 0.10=0.90$. Looking up the z - score in the standard normal distribution table (or using a calculator with a normal - distribution function), the z - score corresponding to an area of 0.90 (or a right - tail area of 0.10) is approximately 1.28 (and - 1.28 for the left - tail in a two - tailed test). Since we are asked for $Z_{crit}$ (critical z - value) for a two - tailed test, the critical values are $\pm1.28$. But if we consider the magnitude (or the positive critical value for reference in some cases), the $Z_{crit}$ (the value we use to compare with the test statistic, considering the two - tailed nature) has a magnitude of 1.28.

Answer:

The critical z - value ($Z_{crit}$) for a two - tailed test with $\alpha = 20\%$ is $\pm1.28$ (or 1.28 when considering the magnitude for the critical region boundaries).