Eighth-grade math scores on the National Assessment of Educational Progress had a mean of 277 in Nebraska compared to a mean of 271 in New Jersey (H. Wainer and L. Brown, American Statistician, vol. 58, 2004, p. 119).
a. Identify the response variable and the explanatory variable.
b. For white students, the means were 281 in Nebraska and 283 in New Jersey. For black students, the means were 236 in Nebraska and 242 in New Jersey. For other nonwhite students, the means were 259 in Nebraska and 260 in New Jersey. Identify the third variable given here. Explain how it is possible for New Jersey to have the higher mean for each race, yet for Nebraska to have the higher mean when the data are combined. (This is a case of Simpson’s paradox for a quantitative response.)