Question

If the value of the reliability coefficient is 0.36 and the SD for the students’ scores in math test is 10, so the 68% true score confidence interval to the observed score 75 should be…..

A.67- 83
B.69-81
C.70-85
D.68-86

Answer 1

To calculate the 68% true score confidence interval to the observed score, multiply the standard deviation by the square root of 1 minus the reliability coefficient to find the standard error of measurement. Then, subtract the margin of error from the observed score and add the margin of error to the observed score to find the 68% confidence interval.

Step-by-step explanation:

The reliability coefficient and the standard deviation can be used to calculate the 68% true score confidence interval to the observed score. In this case, the reliability coefficient is 0.36 and the standard deviation is 10.

1. First, calculate the standard error of measurement (SEM) by multiplying the standard deviation by the square root of 1 minus the reliability coefficient:

   SEM = 10 * √(1 - 0.36) = 10 * √(0.64) = 8.94

2. Next, calculate the margin of error (MOE) by multiplying the SEM by 1 standard deviation:

   MOE = 8.94 * 1 = 8.94

3. Finally, the 68% true score confidence interval can be found by subtracting the MOE from the observed score and adding the MOE to the observed score:

   68% Confidence Interval = 75 - 8.94 to 75 + 8.94

   68% Confidence Interval = 66.06 to 83.94

Therefore, the correct answer is A. 67-83.