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
A)56; 62
B)53; 65
C)49; 69
D)-3.00; 3.00

Question

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 ​
A)56; 62
B)53; 65 ​
C)49; 69
D)-3.00; 3.00

Quizplus · Accepted Answer

The standard error of measurement (SEM) is calculated using the formula SEM = SD * sqrt(1 - reliability), where SD is the standard deviation and reliability is the reliability coefficient. For this question, SEM = 10 * sqrt(1 - 0.91) = 10 * sqrt(0.09) = 10 * 0.3 = 3. To find the range in which the true score falls 95% of the time, we use the formula: score ± (1.96 * SEM), where 1.96 is the z-score corresponding to 95% confidence interval in a normal distribution. Thus, the range is 59 ± (1.96 * 3) = 59 ± 5.88, which approximately equals 53 to 65.

If the Reliability Coefficient of an Instrument Is