Final answer:
The question incorrectly conflates statistical analysis with care classifications in healthcare. For the statistical analysis part, the hypothesis test involves comparing incidence of disease in a local nursing home with a previous general incidence rate, using a sample of 150 residents with 82 reporting the disease, and applying a z-test for proportions to determine if there is a significant difference.
Step-by-step explanation:
In respect to the student's question about case-mix groups, it appears that there might be some confusion in the question posed, as it mixes different types of inquiry. The question mentioned discusses a scenario in a nursing home and relates to a statistical analysis of an infectious disease prevalence rather than determining a specific case-mix group for a resident which would involve a different set of data including the resident's clinical complexity. However focusing on the statistical component provided, to conduct a hypothesis test to determine if the incidence of an infectious disease in a local nursing home is lower than the 18 percent baseline noted in 2011, we will use the data of 150 randomly surveyed residents, where 82 were found to have the disease. Our null hypothesis (H0) is that the proportion of residents with the disease is at least 18 percent and the alternative hypothesis (Ha) is that this proportion is less than 18 percent. Given the sample size (n=150) and number who have the disease (x=82), the sample proportion (p-hat) is 82/150.
Using a z-test for proportions at a significance level of 0.05, we can calculate the z-score and compare it against the critical value to decide whether to reject H0. Based on this evaluation, we would then conclude if the local incidence of the disease is statistically significantly lower than the referenced 18 percent, or if there's not enough evidence to reject the null hypothesis. Note that actual calculations, including the z-score and p-value need to be executed to achieve the conclusion.