1. The problem is to identify the correct null hypothesis ($H_0$) and alternative hypothesis ($H_1$) for a given mean $\mu$ related to wave height. 2. The null hypothesis ($H_0$) usually represents the status quo or a statement of equality or inequality that we test against. 3. The alternative hypothesis ($H_1$) represents what we want to prove or the opposite of $H_0$. 4. Common forms of $H_0$ include $\mu = c$, $\mu \leq c$, or $\mu \geq c$, where $c$ is a constant. 5. The alternative $H_1$ is then $\mu \neq c$, $\mu > c$, or $\mu < c$ accordingly. 6. Given the options: - $H_0 : \mu > 16.4$ (null hypothesis stating mean is greater than 16.4) - $H_0 : \mu = 16.4$ (null hypothesis stating mean equals 16.4) - $H_0 : \mu \leq 16.4$ (null hypothesis stating mean is less than or equal to 16.4) - $H_1 : \mu = 83.6$ (alternative hypothesis stating mean equals 83.6) 7. Typically, $H_0$ is an equality or inequality including equality, and $H_1$ is a strict inequality or difference. 8. The option $H_0 : \mu \leq 16.4$ is a valid null hypothesis for testing if the mean is at most 16.4. 9. The alternative $H_1$ should be $\mu > 16.4$ if testing for greater mean, but $H_1 : \mu = 83.6$ is unusual and likely incorrect as an alternative hypothesis. 10. Therefore, the correct null hypothesis among the options is $H_0 : \mu \leq 16.4$. Final answer: $H_0 : \mu \leq 16.4$ is the correct null hypothesis.