Question

Determine the critical value(s) for a one-mean $z$-test at the $1\%$significance level if the test is

a. right tailed. b. left tailed

c. two tailed

Short answer

For right tailed, $z_{0.01}=2.33$

For left tailed, $z_{0.01}=-2.33$

For two tailed,$\pm z_{0.01}=\pm 2.575$

Step-by-step solution

Step 1. Right tailed

We determine the critical value for a one-mean $z$-test at the $1\%$significance level if the test is right tailed.

When $\alpha =0.01$, we find normal distribution tables, the critical value of $z_{0.01}=2.33$as shown in the figure below.