Raw scores on behavioral tests are often transformed for easier comparison. A te

Question

Raw scores on behavioral tests are often transformed for easier comparison. A test of reading ability has mean 69 and standard deviation 10 when given to third graders. Sixth graders have mean score 77 and standard deviation 13 on the same test. To provide separate "norms" for each grade, we want scores in each grade to have mean 100 and standard deviation 20. (Round your answers to two decimal places.)

(a) What linear transformation will change third-grade scores x into new scores xnew = a + bx that have the desired mean and standard deviation? (Use b > 0 to preserve the order of the scores.)

(b) Do the same for the sixth-grade scores.

(c) David is a third-grade student who scores 79 on the test. Find David's transformed score.


(d) Nancy is a sixth-grade student who scores 79. What is her transformed score?

Explanation / Answer

a)for new Std deviation =b*SD(X)

20=b*10

b=2

for new mean E(Xnew) =a+bE(x)

100=a+b*69

a=-38

hence a=-38

b=2

b) similarly here a =-18.46

b=1.54

c) transformed score =-38+2*79=120

d) transformed score = -18.46+1.54*79=103.08

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.