1. **State the problem:** We are testing the hypothesis about the population mean $\mu$ with null hypothesis $H_0: \mu = 70.2$ and alternative hypothesis $H_1: \mu \neq 70.2$ at significance level $\alpha = 0.05$. 2. **Given data:** Sample mean $\bar{x} = 73.7$, population standard deviation $\sigma = 11.2$, and significance level $\alpha = 0.05$. 3. **Formula used:** For hypothesis testing of the mean with known population standard deviation, the test statistic $z$ is calculated by: $$ z = \frac{\bar{x} - \mu_0}{\sigma / \sqrt{n}} $$ where $\mu_0$ is the hypothesized mean and $n$ is the sample size. 4. **Important note:** The sample size $n$ is not provided, so we cannot compute the exact test statistic or p-value. However, if $n$ were known, we would proceed to calculate $z$ and compare it to critical values for a two-tailed test at $\alpha=0.05$ (critical values approximately $\pm 1.96$). 5. **Interpretation:** If $|z| > 1.96$, we reject $H_0$; otherwise, we fail to reject $H_0$. Since $n$ is missing, the problem cannot be fully solved without it.