Consider the following hypothesis,
\[
\begin{array}{l}
H_{0}: \mu=7, \quad \mathrm{~S}=5, \quad \bar{X}=5, \quad \mathrm{n}=46 \\
H_{a}: \mu \neq 7
\end{array}
\]

What is the rejection region (step 3).

Step 1 ：Given the following hypothesis, \(H_{0}: \mu=7, \quad \mathrm{~S}=5, \quad \bar{X}=5, \quad \mathrm{n}=46 \) and \(H_{a}: \mu \neq 7\)

Step 2 ：The rejection region is the range of values for which we would reject the null hypothesis. To find this, we first need to calculate the test statistic (Z score) and then find the critical values for a given level of significance (usually 0.05). The rejection region would be any value that is less than the lower critical value or greater than the upper critical value.

Step 3 ：The formula for the test statistic in a one-sample Z test is: \(Z = (\bar{X} - \mu) / (S/√n)\)

Step 4 ：Given the sample mean (\(\bar{X} = 5\)), the population mean under the null hypothesis (\(\mu = 7\)), the standard deviation (\(S = 5\)), and the sample size (\(n = 46\)), we can calculate the test statistic.

Step 5 ：After calculating the test statistic, we can find the critical values. For a two-tailed test with a significance level of 0.05, the critical values are approximately -1.96 and +1.96.

Step 6 ：The rejection region would be \(Z < -1.96\) or \(Z > +1.96\).

Step 7 ：Let's check if our test statistic falls in the rejection region. The test statistic \(Z\) is approximately -2.71, which is less than the lower critical value of -1.96. Therefore, it falls in the rejection region.

Step 8 ：Final Answer: The rejection region is \(\boxed{Z < -1.96 \text{ or } Z > +1.96}\). Since our test statistic \(Z = -2.71\) falls in this region, we would reject the null hypothesis.