Question

determine the critical value. using the z - tables (or t - tables), determine the critical value for the left - tailed z - test with α = 0.01 - 2.576 2.576 2.326 - 2.326

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 (the cumulative distribution function of the standard normal distribution \(Z\sim N(0,1)\)), we find the \(z\) - value corresponding to a cumulative probability of \(0.01\).

Answer:

\(- 2.326\)