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
I see you haven't resolved this question about whose score you want. Please check with your teacher about this.
http://www.jiskha.com/display.cgi?id=1374878955
Do you mean standard error (SEm) or standard deviation (SD).
SEm = SD/√n, but no n is indicated.
If you meant SD, then use this equation.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.0025 or .4975) and its Z score.
With equation above, calculate score for both ± Z.
you must add or subtract the SEM 3 times.
72-9=63
72+9=81
d. 63-81
To determine where we would expect Tom's true score to fall, we need to use the concept of the "confidence interval." The confidence interval is a range of values within which an individual's true score is likely to fall with a certain level of confidence.
In this case, we have Joe's score of 72 on the Counseling Aptitude Scale and the standard error of measurement (SEM) of the scale is 3.
To calculate the confidence interval, we can use the formula:
Confidence Interval = Score ± (Z * SEM)
Where:
- "Score" is Joe's score (72 in this case)
- "Z" is the z-score corresponding to the desired level of confidence (99.5% in this case)
- "SEM" is the standard error of measurement (3 in this case)
The z-score represents the number of standard deviations from the mean of a normally distributed variable. The z-score values depend on the desired level of confidence, and for 99.5% confidence interval, the z-score is approximately 2.81 (obtained from a standard normal distribution table or a statistical software).
Now, let's calculate the confidence interval:
Confidence Interval = 72 ± (2.81 * 3)
= 72 ± 8.43
= [72 - 8.43, 72 + 8.43]
= [63.57, 80.43]
Therefore, we would expect Tom's true score to fall within the range of 63.57 to 80.43, rounded to 2 decimal places.
Among the given options, the closest range is option d) 63 to 81.