"Early Television Exposure and Subsequent Attentional Problems in Children," published in Pediatrics in April 2004, investigated television-watching habits of 1,278 children aged 1 and 1,345 children aged 3 in the early 1990s. "Our main outcome was the hyperactivity subscale of the Behavioral Problems Index determined on all participants at age 7. Children who were
1.2 standard deviations above the mean were classified as having attentional problems. Our main predictor was hours of television watched daily at ages 1 and 3 years. [. . .] Children watched an average of 2.2 hours (SD: 2.91) of television per day at age 1 and 3.6 hours (SD: 2.94) per day at age 3."24
a. Tell what the main explanatory variable is, and whether it is quantitative or categorical.
b. Tell what the main response variable is, and whether it is quantitative or categorical.
c. One of these is the percentage of children who were classified as having attentional problems (those whose values were 1.2 or more standard deviations above the mean). Use what you know from the 68-95-99.7 Rule to tell which one it is: top 1.2%, top 2.1%, top 12%, or top 21%.
d. Explain why confidence intervals can be set up based on probabilities from the z distribution.
e. Report a 95% confidence interval for mean daily television hours watched by all children at age 1.
f. Explain why a 95% confidence interval for mean daily television hours watched by all children at age 3 would have a different center but roughly the same width.
g. The study found that "A 1-SD increase in the number of hours of television watched at age 1 is associated with a 28% increase in the probability of having attentional problems at age 7." Tell which one of these is not a correct interpretation, and why:
1. Children who had attentional problems at age 7 tended to have watched more TV at age 1.
2. Watching more TV at age 1 caused attentional problems at age 7.
3. Children who watched more TV at age 1 were more likely to have attentional problems at age 7.
4. Children who watched less TV at age 1 were less likely to have attentional problems at age 7.