# Test and Measurements Task

See attached chart. Your assistance is greatly appreciated. Thank you.

TASK

You have been provided the z-scores of three individuals.

1. Person A received a z-score of 1.0.

2. Person B received a z-score of 0

3. Person C received a z-score of -1.0.

Using Figure above (see attchement), indicate each individual's score as a T score, CEEB score, IQ score, and approximate percentile score. Once you have indicated these transformed scores, in 1-2 pages, describe why it is possible to easily convert standard scores from one scale to another. Include in your answer the mean and standard deviation of each of the transformed scores and the theoretical rationale for their equivalency.

© BrainMass Inc. brainmass.com June 3, 2020, 11:54 pm ad1c9bdddfhttps://brainmass.com/statistics/z-test/test-and-measurements-task-306957

#### Solution Preview

Let's take a closer look.

RESPONSE:

You have been provided the z-scores of three individuals.

1. Person A received a z-score of 1.0.

2. Person B received a z-score of 0

3. Person C received a z-score of -1.0.

I. Using the Figure above, indicate each individual's score as a T score, CEEB score, IQ score, and approximate percentile score.

Therefore, referring to the conversion chart it is just a matter of locating the z-score and following it down to see what it converts to for the t-score, etc. The standard deviations are preset (see more detail below) for each score, which are calculated below based on the z-score equation. For example:

1.Person A received a z-score of 1.0: T score (60), CEEB score (600), IQ score (115), Subset scores (13), and approximate percentile score (84).

Standard deviations: A z-score of 1 has a standard deviation of 1; T-score of 60 (sd=5z or 5); CEEB score of 600 (sd=3z or 3); Wechsler IQ (sd= 15z or 15); Subset scores of 7(sd=3z or 3)

2. Person B received a z-score of 0: T score (50), CEEB score (500), IQ score (100), Subset scores (10), and approximate percentile score (50).

Standard deviations: A z-score of 0 has a standard deviation of 0; T-score of 50 (1sd=5z or 0); Wechsler IQ of 100 ...

#### Solution Summary

Using the attached figure Figure, this solution transforms z-scores to T score, CEEB score, IQ score, and approximate percentile score, including the mean and standard deviation of each of the transformed scores and the theoretical rationale for their equivalency. It also describes why it is possible to easily convert standard scores from one scale to another.