3.13 Data on fifth-grade test scores (reading and mathematics) for 400 school districts in Brussels yield average score Y = 712.1 and standard deviation sY = 23.2.

a. Construct a 90% confidence interval for the mean test score in the population.

b. When the districts were divided into districts with small classes 1 6 20 students per teacher) and large classes 1 Ú 20 students per teacher), the following results were found:

Class Size Average Salary 1Y2 Standard Deviation 1sY2 n Small 721.8 24.4 150 Large 710.9 20.6 250 Is there statistically significant evidence that the districts with smaller classes have higher average test scores? Explain.