An individual being tested for a gifted program scores a 132 on the Cognitive Ability Test (CogAT), which has a mean of 100 and a standard deviation of 16. There is a .40 correlation between the CogAT score and success as measured by GPA in the gifted program, which has a weighted mean of 4.3 with a SD of .2. Use the Standard Error of the Estimate (SE_est) to predict where this students GPA will fall 95 percent of the time. A) 4.7 ± .36 B) 4.3 ± .4 C) 4.5 ± .8 D) 4.7 ± .28 E) None of these

Question

Quizplus · Accepted Answer

The Standard Error of the Estimate (SEest) is used to predict the range within which a student's GPA will fall, given their CogAT score. The formula for SEest is:SEest = SD of GPA * √(1 - r²)where:SD of GPA is the standard deviation of the GPA in the gifted programr is the correlation between the CogAT score and success as measured by GPAIn this case, the SD of GPA is .2 and the correlation between the CogAT score and success as measured by GPA is .40. Therefore, the SEest is:SEest = .2 * √(1 - .40²) = .12To predict where this student's GPA will fall 95 percent of the time, we need to multiply the SEest by 1.96, which is the z-score for a 95% confidence interval. Therefore, the range within which the student's GPA will fall 95 percent of the time is:4.3 ± 1.96 * .12 = 4.3 ± .23Therefore, the correct answer is A) 4.7 ± .36.

An Individual Being Tested for a Gifted Program Scores a 132