Question

using the z table (the standard normal distribution table), find the critical value (or values) for the two - tailed test with \\( \alpha=0.03 \\). round to two decimal places, and enter the answers separated by a comma if needed. critical value(s):

Explanation:

Step1: Calculate the area in each tail

For a two - tailed test with $\alpha = 0.03$, the area in each tail is $\frac{\alpha}{2}=\frac{0.03}{2}=0.015$.

Step2: Find the z - score

We look for the $z$ - score such that the area to the left of it is $1 - 0.015=0.985$.
Using the standard normal distribution table (z - table), the $z$ - score corresponding to an area of $0.985$ is approximately $2.17$.
Since it is a two - tailed test, the critical values are $\pm z$. So the critical values are $- 2.17$ and $2.17$.

Answer:

$\pm 2.17$