Question

Two-tailed test, o? is known, a= 0.05, n= 45

Answer 1

The following null and alternative hypotheses need to be tested:

$H_0:\mu=\mu_0$

$H_1:\mu\not=\mu_0$

This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

Based on the information provided, the significance level is $\alpha = 0.05,$ and the critical value for a two-tailed test is $z_c = 1.96.$

The rejection region for this two-tailed test is $R = \{z: |z| > 1.96\} .$

The z-statistic is computed as follows:

$$z=\dfrac{\bar{x}-\mu_0}{\sigma/\sqrt{n}}$$