Question: Social interaction of mental patients. The Community Mental Health Journal (August 2000) presented the results of a survey of over 6,000 clients of the Department of Mental Health and Addiction Services (DMHAS) in Connecticut. One of the many variables measured for each mental health patient was frequency of social interaction (on a 5-point scale, where 1 = very infrequently, 3 = occasionally, and 5 = very frequently). The 6,681 clients who were evaluated had a mean social interaction score of 2.95 with a standard deviation of 1.10.
(a) Conduct a hypothesis test (at α = .01) to determine if the true mean social interaction score of all Connecticut mental health patients differs from 3.
(b) Examine the results of the study from a practical view, then discuss why ‘‘statistical significance'' does not always imply ‘‘practical significance.''
(c) Because the variable of interest is measured on a 5-point scale, it is unlikely that the population of ratings will be normally distributed. Consequently, some analysts may perceive the test, part a, to be invalid and search for alternative methods of analysis. Defend or refute this position.