A study performed by Florida International University investigated how musical instruction in an after-school program affected overall competence, confidence, caring, character, and connection

(known as the “Five Cs”). The study compared a group of students who received music instruction to another group who didn’t. One of the findings was that those receiving music instruction showed, on average, a significant increase in their character. Character was measured by scoring answers to questions such as “I finish whatever I begin,” with scores ranging from 1 (“not at all like me”) to 5 (“very much like me”). For each part, select (i) or (ii).

a. For the two groups to be called significantly different, the difference in the average character scores computed from the participants in the study had to be

(i) much smaller or (ii) much larger than one would expect under regular sample-to-sample variability.

b. What does a significant increase imply in this context?

That the difference in the average score to questions such as “I finish whatever I begin” between the group receiving music instruction and the group that didn’t was (i) much larger than would be expected if music instruction didn’t have an effect or (ii) nearly identical in the two groups.

c. Suppose the two groups did not differ significantly in terms of the average confidence score. This indicates that the difference in the average confidence score of participants (i) can be explained by regular sample-to-sample variability or (ii) cannot be explained by regular sample-to-sample variability.