Reading scores in Dallas. The Trial Urban District Assessment (TUDA) is a govern
ID: 3386085 • Letter: R
Question
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?Explanation / Answer
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]
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