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 65 and standard deviation 5 when given to third graders. Sixth graders have mean score 90 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 linear transformation will change third-grade scores x into new scores xnew = a + bx that have the desired mean and standard deviation? (Use b>O 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 78 on the test. Find David's transformed score. Nancy is a sixth-grade student who scores 78. What is her transformed score? Who scores higher within his or her grade? Nancy O David

Explanation / Answer

a) here as std deviation(xnew) =b*std deviation

20=b*5

b=4

and mean (xnew) =a+4*E(x)

100 =a+4*65

a=-160

b) similarly a =-100

and b=2.2222

c)

transformed score =-160+78*4=152

d) transformed score =-100+2.2222*78=73.3316

David score

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