Question

Motivated by findings from California that school districts with lower student-teacher ratios have higher average test scores, administrators in New York City recently reviewed the relationship between school- level student-teacher ratios and average test scores within their population of elementary schools. Data for fifth-grade test scores (reading and math) from 1,575 elementary schools yield Y ̄ = 631.7 and sY = 17.8

a) Construct a 95% confidence interval for the mean test score in the population (i.e., of schools in NYC).

b) When NYC administrators divided the population into schools with small (i.e., < 20) and large (i.e., ≥ 20) average class sizes, the 555 schools with small classes had a mean test score of 644 with a standard deviation of 11.7, while the 1,020 schools with large classes had a mean test score of 625 with a standard deviation of 21.1. Is there statistically significant evidence that the schools with smaller class sizes have higher average test scores? Explain.

c) Do these results (likely) represent a causal estimate? Why or why not?

Answer 1