If a student received a score of 50 on a math test with a standard error of measurement of 3,which of the following statements would be TRUE of the "true score"?
A) In 68% of the cases, the "true score" would be expected to be between 44 and 56.
B) In 68% of the cases, the "true score" would be expected to be between 47 and 53.
C) In 95% of the cases, the "true score" would be expected to be between 47 and 53.
D) In 95% of the cases, the "true score" would be expected to be between 44 and 56.

Question

Quizplus · Accepted Answer

To find the range of "true score" within a certain level of confidence, we can use the formula:
True score range = Observed score ± (Critical value × Standard error of measurement)
For a 68% confidence level, the critical value is 1, and for a 95% confidence level, the critical value is 1.96 (using a normal distribution). 
So, for a score of 50 with a standard error of 3:
68% confidence interval: 50 ± (1 × 3) = 47 to 53
95% confidence interval: 50 ± (1.96 × 3) = 44.12 to 55.88
Since none of the choices match the 95% confidence interval exactly, the closest answer is B, which includes the middle 68%.

If a Student Received a Score of 50 on a Math