The Trial Urban District Assessment (TUDA) is a government-sponsored study of student achievement in large urban school districts. TUDA gives a reading test scored from 0 to 500. A score of 243 is a “basic” reading level and a score of 281 is “proficient.” Scores for a random sample of 1470 eighthgraders in Atlanta had a mean of 240 with standard deviation of 42.17.

a. Construct and interpret a 99% confidence interval for the mean reading test score of all Atlanta eighth-graders.

b. Based on your interval from part (a), is there convincing evidence that the mean reading test score for all Atlanta eighthgraders is less than the basic level? Explain your answer.