An article entitled “Piano Lessons Boost Math Scores” states that “second-grade students who took piano lessons for four months scored significantly higher on math than children who did not.”26 a....

An article entitled “Piano Lessons Boost Math Scores” states that “second-grade students who took piano lessons for four months scored significantly higher on math than children who did not.”26

a. Tell why these results are more convincing if they are based on an experiment than they would be if they were based on an observational study.

b. One possible design is to take a sample of second graders and randomly assign some to be given piano lessons for 4 months, and others not. Is this a two-sample or a paired design?

c. Another possible design is to take a sample of second-grade twins and randomly assign one twin to be given piano lessons for 4 months, the other not. Is this a two-sample or a paired design?

d. Explain why the design described in part (c) could do a better job at pinpointing the effects of piano lessons on math skills, compared to the design described in part (b).

e. If an experiment is carried out to determine if piano lessons can increase math scores, is it important for the researchers who evaluate the response to be unaware of whether or not a student was in the treatment group?