Exam 7: Sampling: Estimating the Frequency of Behaviors and Beliefs

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Dr. Dowling is a clinical psychologist who is interested in the link between mental illness and criminal activity. She gets IRB permission to study patients at all five inpatient/residential mental health facilities in her state. There are 4,307 patients currently living in these facilities. She asks patients whether they have ever been arrested for a crime and whether they have ever been convicted of a crime. She collects a sample size of 1,369. She finds that 27% (+/− 3%) report having been arrested for a crime but that only 13% (+/− 3%) have been convicted of a crime. Dr. Dowling is interviewed by a journalist about the findings of her study. The journalist asks Dr. Dowling how many people live in all five hospitals and Dr. Dowling answers. The journalist replies that given that there are only about 4,000 people, it seems reasonable that Dr. Dowling should have studied the entire population rather than just drawing a sample for her study to really tell us something about people suffering from mental illness. How should Dr. Dowling respond?