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 53 and standard deviation 10 when given to third graders. Sixth graders have mean score 79 and standard deviation 7 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 =

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

b =

(c) David is a third-grade student who scores 71 on the test. Find David's transformed score.

(d) Nancy is a sixth-grade student who scores 71. What is her transformed score?

Who scores higher within his or her grade?

__ Nancy

__ David    

b =

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

b =

(c) David is a third-grade student who scores 71 on the test. Find David's transformed score.

(d) Nancy is a sixth-grade student who scores 71. What is her transformed score?

Who scores higher within his or her grade?

__ Nancy

__ David    

Explanation / Answer

3--> Mean, stdev = (53,10)
6--> (79,7)
New norms--> (100,20)

a) and b)

We first calc. Z for 3rd grader.
Z = X-53 / 10
Then we move it to New norms, ((X-53)/10 )*20+100
So, 2X-10.6+100 = 2X+89.4
So, a = 89.4, b=2

We first calc. Z for 6rd grader.

Z = X-79 / 7
Then we move it to New norms, ((X-79)/7 )*20+100
So, =2.86X-27.65+100
So, b = 2.86, a=72.35

c) and d)

Davids' transformed score is 89.4+2*71=231.4 ( use this because he' in3rd grade)

Nancy' transformed score is 2.86*71+72.35=275.41  ( use this because she' in 6th grade)

So, Nancy' ( 6th grade score of 71) transformed score is more than Davids( 3rd grade score of 71)

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