Solution: We are given:
[tex]\bar{x}=117, \sigma=25, n=48, \alpha=0.01[/tex]
The hypotheses under consideration is:
[tex]H_{0}:\mu=123[/tex]
[tex]H_{A}:\mu\neq123[/tex]
First let's find the critical value at [tex]\alpha=0.01[/tex].
Since the alternative hypothesis is two tailed, therefore we will have two critical values.
Also, since the population standard deviation is given, therefore we will use standard normal distribution to find the critical value.
Using the standard normal table, the critical values are:
[tex]z_{critical}=-2.58,2.58[/tex]
Therefore, decision rule in terms of the critical values of the test statistic is:
Reject the null hypothesis if the calculated value of the test statistic, z is not contained within the critical values, [tex]-2.58,2.58[/tex]. Otherwise do not reject the null hypothesis.
