Do piano lessons improve the spatial-temporal reasoning of preschool children? A study designed to investigate this question measured the spatial-temporal reasoning of a random sample of 34 preschool children before and after 6 months of piano lessons. The difference (After − Before) in the reasoning scores for each student has mean 3.618 and standard deviation 3.055.

a. Construct and interpret a 90% confidence interval for the true mean difference.

b. Based on your interval from part (a), can you conclude that taking 6 months of piano lessons would cause an increase in preschool students’ average reasoning scores? Why or why not?