Final answer:
The nurse provided an operational definition of depression by setting a threshold of a score above 7 on the Hamilton Depression Rating Scale. This allows for quantifiable measurement in research. In addition, when conducting a hypothesis test for the proportion of people suffering from depression in a town versus the general population, one tests a single proportion and establishes a null and alternative hypothesis.
Step-by-step explanation:
The nurse wrote an operational definition. An operational definition specifies the measurement conditions for the application of a term by defining the term in terms of observable and quantifiable phenomena.
In the context of the nurse's research, the operational definition of depression is a patient reporting a score above 7 on the Hamilton Depression Rating Scale. It sets a clear threshold that can be consistently measured across the study, which in this case helps to identify patients who are considered to be experiencing depression.
Addressing the question concerning the National Institute of Mental Health's statistics and the town survey:
- This is a test of one proportion, as it compares the proportion of people in the town suffering from depression to the known proportion in the general adult American population.
- The null hypothesis (H0) is that the proportion of people in the town with depression is equal to or greater than 9.5 percent. The alternative hypothesis (Ha) is that the proportion of people in the town with depression is less than 9.5 percent.