Joe had a score of 72 on the Counseling Aptitude Scale, and the standard error of measurement of the scale is 3. Where would we expect Tom's true score to fall 99.5 percent of the time?
a.71 to 73
b. 69 to 75
c. 66 to 78
d. 63 to 81
Joe? Tom?
For Tom
Did Tom have a score of 72?
Thats were I got confused. I was thinking he did but could it be wrong
90
3+3+3=9, so D 63 to 81 is the answer for 99.5% of the time.
To determine where we would expect Tom's true score to fall 99.5 percent of the time, we can use the standard error of measurement (SEM) and a confidence interval.
The formula to calculate the confidence interval for a given percentage is:
Confidence Interval = Tom's score ± (Z score × SEM)
In this case, since we want to find the interval where Tom's true score would fall 99.5 percent of the time, we need to find the appropriate Z score for a 99.5% confidence level.
To find the Z score, we can use a Z table or a statistical calculator. For a 99.5% confidence level, the Z score is approximately 2.81.
Now, we can calculate the confidence interval using the formula:
Confidence Interval = 72 ± (2.81 × 3)
Calculating the values:
Lower Limit = 72 - (2.81 × 3) ≈ 63.57
Upper Limit = 72 + (2.81 × 3) ≈ 80.43
Therefore, Tom's true score would be expected to fall between 63.57 and 80.43 with 99.5 percent confidence.
Among the given options, the answer that includes this interval is option d. 63 to 81.