Question

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 eighth-graders in Atlanta had a mean of 240 with standard deviation of 42.17.

Construct and interpret a 99% confidence interval for the mean reading test score of all Atlanta eighth-graders. Show your calculations and round your interval to three decimal places.

Answer 1

There is a 99% chance that the value may fall between 237.167 and 242.833

What is confidence interval?

Confidence interval shows the range of values for which a random sample might be.

The z score of 99% confidence interval is 2.576. sample = 1470, mean = 240 and standard deviation = 42.17. Hence, margin of error (E) is:

$E = z_\frac{\alpha }{2}*\frac{standard\ deviation}{\sqrt{sample\ size} } =2.576*\frac{42.17}{\sqrt{1470} } =2.833$

The confidence interval = mean ± E = 240 ± 2.833 = (237.167, 242.833)

There is a 99% chance that the value may fall between 237.167 and 242.833

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