NAEP scores In 2015, eighth-grade math scores on the National Assessment of Educational Progress had a mean of 283.56 in Maryland compared to a mean of 284.37 in Connecticut (Source: http://nces.ed.gov/nationsreportcard/

naepdata/dataset.aspx).

a. Identify the response variable and the explanatory variable.

b. The means in Maryland were respectively 274, 284, 285, 291 and 294 for people who reported the number of pages read in school and for homework, respectively as 0–5, 6–10, 11–15, 15–20 and 20 or more. These means were 270, 281, 284, 289 and 293 in Connecticut. Identify the third variable given here. Explain how it is possible for Maryland to have the higher mean for each class, yet for Connecticut to have the higher mean when the data are combined. (This is a case of Simpson’s paradox for a quantitative response.)