1. The problem is to identify the correct alternative hypothesis $H_1$ from the given options involving the population mean $\mu$ and the value 16.4. 2. In hypothesis testing, the null hypothesis $H_0$ usually states a condition of equality or no effect, while the alternative hypothesis $H_1$ states what we want to test for, such as inequality or difference. 3. The four options given are: - $H_1: \mu \geq 16.4$ - $H_1: \mu < 16.4$ - $H_1: \mu > 16.4$ - $H_1: \mu = 16.4$ 4. Typically, the alternative hypothesis is a strict inequality ($<$ or $>$) or sometimes a two-sided inequality ($\neq$), but not an equality. 5. Therefore, the correct forms for $H_1$ are either $\mu < 16.4$ or $\mu > 16.4$, depending on the context of the test. 6. The options $H_1: \mu \geq 16.4$ and $H_1: \mu = 16.4$ are not standard alternative hypotheses because they include equality or are equalities, which belong to the null hypothesis. Final answer: The valid alternative hypotheses are $H_1: \mu < 16.4$ or $H_1: \mu > 16.4$ depending on the test direction.