Question

In each of Exercises 9.41-9.46 ,determine the critical values for a one-mean z-test. For each exercise, draw a graph that illustrates your answer

A two-tailed test with$\alpha =0.05$

Short answer

Here we set the $\alpha =0.05$value level of the given test that describes z with a two-tailed view. For a single z-definition test, under the null hypothesis, z-test statistics have a fairly common distribution.

z-check. In each test Two double-tailed tail tests, we have a drop point on both sides of the regular curve.

Therefore the value of two z points divides the area below the normal curve into the central area of 0.95 and the two areas outside of 0.025

That means key values $\pm z_{0.025}$

Used for areas under the standard curve table, $\pm z_{0.025}=\pm 1.96$.

Step-by-step solution

Step 1. Given 

A two -tailed test with$\alpha =0.05$

Step 2. Graph 

Here we set the $\alpha =0.05$value level of the given test that describes z with a two-tailed view. For a single z-definition test, under the null hypothesis, z-test statistics have a fairly common distribution.

z-check. In each test Two double-tailed tail tests, we have a drop point on both sides of the regular curve.

Therefore the value of two z points divides the area below the normal curve into the central area of 0.95 and the two areas outside of 0.025

That means key values $\pm z_{0.025}$

Used for areas under the standard curve table, $\pm z_{0.025}=\pm 1.96$

The rejection position is therefore found as in the following graph