Question

multiple choice 4 points
determine the critical value.
using the z - tables (or t - tables), determine the critical value for the left - tailed z - test with \\( \alpha = 0.01 \\)
-2.326
2.326
2.576
-2.576

Explanation:

Step1: Recall the property of left - tailed z - test

For a left - tailed z - test, the critical value \(z_{\alpha}\) is the value such that \(P(Z<z_{\alpha})=\alpha\).

Step2: Use the standard normal distribution table (z - table)

We are given \(\alpha = 0.01\). Looking up the value in the standard normal distribution table (z - table), we find the z - score corresponding to an area of \(0.01\) in the left - tail.
The standard normal distribution is symmetric about \(z = 0\). The area to the left of \(z=- 2.326\) is approximately \(0.01\) (from the z - table: \(P(Z < - 2.33)\approx0.0099\) and \(P(Z < - 2.32)\approx0.0102\), and by interpolation or using more precise tables, the value is \(z=-2.326\)).

Answer:

• 2.326