A student has a score of 80 on a class test with a score reliability of .84 and a standard deviation of 10.What is the band within which the student's true score is likely to fall? (Use the .95 confidence level).
A) 70 and 90
B) 72 and 88
C) 75 and 85
D) 76 and 84

Question

Quizplus · Accepted Answer

To find the band within which the student's true score is likely to fall, we need to use the formula:
True score = Observed score + (Error x reliability)
where error = (z-score x standard error), z-score = 1.96 (for 95% confidence level), and standard error = standard deviation / sqrt(sample size)
Assuming the sample size is 1 (since we have only one student), the calculation would be:
True score = 80 + (1.96 x 10 / sqrt(1) x 0.84)
True score = 80 + 2.6016
True score = 82.6
Therefore, we can say with 95% confidence that the student's true score is likely to fall within the range of 72 and 88 (80 +/- 2.6), which corresponds to choice B.

A Student Has a Score of 80 on a Class