Final answer:
The question pertains to statistical hypothesis formulation for comparing the means of different groups. A null hypothesis represents no effect or difference, while an alternative hypothesis indicates the suspected effect or difference.
Step-by-step explanation:
The question provided is regarding the formulation of statistical hypotheses, specifically for comparing means of treated and untreated patients or general population means. In hypothesis testing, the appropriate hypotheses typically consist of a null hypothesis (H0) and an alternative hypothesis (Ha). The null hypothesis is a statement of no effect or no difference, which we test against an alternative hypothesis that states there is an effect or a difference.
For example, if we suspect that treated patients have a different outcome compared to untreated ones, the null hypothesis might be H0: μ_t = μ_ut (no difference between the two groups), and the alternative hypothesis might be Ha: μ_t ≠ μ_ut (there is a difference). Similarly, if we want to check if a new treatment leads to better outcomes than no treatment, we might have H0: μ_t ≤ μ_ut vs. Ha: μ_t > μ_ut. The choice of hypotheses will depend on the context of the research and what is being tested. Proper understanding of hypotheses testing is critical for conducting meaningful research and obtaining valid conclusions.