Motivated by findings from California that school districts withlower student-teacher ratios have higher average test scores,administrators in New York City recently reviewed the relationshipbetween school- level student-teacher ratios and average testscores within their population of elementary schools. Data forfifth-grade test scores (reading and math) from 1,575 elementaryschools yield Y ? = 631.7 and sY = 17.8
a) Construct a 95% confidence interval for the mean test scorein the population (i.e., of schools in NYC).
b) When NYC administrators divided the population into schoolswith small (i.e., < 20) and large (i.e., ? 20) average classsizes, the 555 schools with small classes had a mean test score of644 with a standard deviation of 11.7, while the 1,020 schools withlarge classes had a mean test score of 625 with a standarddeviation of 21.1. Is there statistically significant evidence thatthe schools with smaller class sizes have higher average testscores? Explain.
c) Do these results (likely) represent a causal estimate? Why orwhy not?
