If the reliability coefficient of an instrument is .91, and the standard deviation is 10, then a client's score of 59 could be interpreted that 95 percent of the time his/her true score will fall between _____ and _____ using standard error of measurement

Question

Quizplus · Accepted Answer

To find the interval within which the true score of the client falls, we use the formula:
True Score = Observed Score +/- (SEM x z-score)
SEM = standard deviation * sqrt(1 - reliability coefficient)
Where z-score for a 95% confidence interval is 1.96
Plugging in the values given, we get:
SEM = 10 * sqrt(1 - 0.91) = 3.16
True Score = 59 +/- (3.16 x 1.96) = 59 +/- 6.21
Therefore, the interval within which the true score falls is 52.79 to 65.21. The closest choice is B, 53 and 65.

If the Reliability Coefficient of an Instrument Is