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 72 and standard deviation 10 when given to third graders. Sixth graders have mean score 84 and standard deviation 9 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 near transformation will change third-grade scores x into new scores x_new = 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 75 on the test. Find David's transformed score. Nancy is a sixth-grade student who scores 75 What is her transformed score? Who scores higher within his or her grade? David Nancy

Explanation / Answer

for linear transformation std deviaiton of Xnew =b*X

hence 20=b*10

b=2

also

E(Xnew)=a+bE(X)

100=a+2*72

a=-44

b) here 20=b*9

b=20/9=2.2222

also 100=a+2.222*84

a=-86.667

c) david score =-44+2*75=106

nancy score =-86.667+2.222*75=80

hence David score is better

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