1. The problem is to understand the null hypothesis $H_0$ and the alternative hypothesis $H_1$ in hypothesis testing. 2. The null hypothesis $H_0$ is a statement that there is no effect or no difference, and it is what we assume to be true until we have evidence to the contrary. 3. The alternative hypothesis $H_1$ is what you want to prove; it represents a new effect or difference. 4. Typically, $H_0$ and $H_1$ are mutually exclusive and cover all possible outcomes. 5. For example, if testing whether a mean equals a value $\mu_0$, then: $$H_0: \mu = \mu_0$$ $$H_1: \mu \neq \mu_0$$ 6. The exact form of $H_0$ and $H_1$ depends on the problem context. 7. To proceed, you need to specify what the hypotheses are about (e.g., mean, proportion, difference). Final answer: $H_0$ and $H_1$ are statements used in hypothesis testing where $H_0$ is the default assumption and $H_1$ is the claim you want to test.