"Inmate's Rising I.Q. Score Could Mean His Death," published in the New York Times in 2004, described the situation of death row inmate Daryl Atkins, who killed a man in Virginia in 1996 after forcing him to withdraw money from an ATM. The U.S. Supreme Court ruled in Atkins v. Virginia in 2003 that it is unconstitutional to execute the mentally retarded, for which the cutoff in Virginia is an IQ score of 70. In 1998, Atkins' IQ was recorded to be 59, but a defense expert retested it in 2004 to be 74, and in 2005 to be 76. A clinical psychologist on the case said that the more recent scores should be discounted because they were the result of "a forced march towards increased mental stimulation" provided by the case itself: "Oddly enough, because of his constant contact with the many lawyers that worked on his case, Mr. Atkins received more intellectual stimulation in prison than he did during his late adolescence and early adulthood. That included practicing his reading and writing skills, learning about abstract legal concepts and communicating with professionals." The article explains that there are other reasons why Atkin's IQ score may have risen: "I.Q. points are rarely completely stable and can drift, though within a relatively narrow range, typically by 5 points up or down. Psychologists recognize that practice drives scores higher. And I.Q.'s tend to rise over time, by about three points a decade."14
a. The article suggests that if you set up a prediction interval for a second IQ score in roughly the same time period, it would be centered at the first IQ score but there would be some variation. Does the number 5 describe the margin of error or the width of the prediction interval?
b. Based on the fact that Atkins scored 74 in 2004, is it plausible that another IQ test around the same time would yield a score less than 70?
c. Is it less plausible that another IQ test would yield a score less than 70, based on the fact that he also scored 76 in 2005?
d. Is the change from 59 in 1998 to 74 in 2004 and 76 in 2005 better explained by increased intellectual stimulation during that period or by the fact that IQ's tend to rise by about three points a decade?