Question

The Trial Urban District Assessment (TUDA) is a government sponsored study of student achievement in large urban school districts. TUDA includes a reading test score from 0 to 500, with a score of 254 considered a “basic” reading level and a score of 292 considered “proficient”. Reading test scores for a random sample of 80 eighth graders in the Dallas school district had a sample mean of 259, with a sample standard deviation of 37.4.

a) Based on this sample data, use an appropriate theoretical distribution to find a 95% confidence interval for the mean reading test score of eighth grade students in Dallas. Conduct a complete analysis and interpret your interval estimate in context of the study. (continued)

b) Based on this interval, is it plausible (i.e., “reasonably likely”) that the mean reading test score of all eighth grade students in Dallas is below the “basic” reading level of 254? Explain your answer.

c) If the school district wants a 95% confidence interval and a margin of error of no more than 5 points, how many students would need to be included in the sample?

Answer 1