Reading scores in Dallas The Trial Urban District Assessment

Reading scores in Dallas. 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 1400 eighth-graders in Dallas had x = 248 with standard error 1.0.^17 (a) We don\'t have the 1400 individual scores, but use of the t procedures is surely safe. Why? (b) Give a 99% confidence interval for the mean score of all Dallas eighth-graders. (Be careful: the report gives the standard error of x, not the standard deviation s.) (c) Urban children often below the basic t the mean for all the basic level?

Solution

A)

Because we have a large sample size, 1400, and we have the summary of data, the sample mean and standard error.

b)

Note that              
              
Lower Bound = X - t(alpha/2) * se              
Upper Bound = X + t(alpha/2) * se              
              
where              
              
df =    1400          
X = sample mean =    248          
t(alpha/2) = critical t for the confidence interval =    2.579348152          
se = standard error =    1          
              
Thus,              
              
Lower bound =    245.4206518          
Upper bound =    250.5793482          
              
Thus, the confidence interval is              
              
(   245.4206518   ,   250.5793482   ) [ANSWER]

c)

Yes, because the whole confidence interval is above 243. [ANSWER]