Scores on the SAT test have a mean of 1518 and a standard deviation of 325. Scores on the ACT test have a mean of 21.1 and a standard deviation of 4.8. Which of the following choices is not true?
A) The SAT score of 1490 is relatively better than the ACT score of 17.0.
B) An ACT score of 17.0 has a z score of -0.85.
C) The ACT score of 17.0 is relatively better than the SAT score of 1490.
D) An SAT score of 1490 has a z score of -0.09.

Question

Quizplus · Accepted Answer

Since the mean and standard deviation of the two tests are different, we cannot directly compare the scores. We need to use z-scores to compare them. A z-score measures how many standard deviations a value is from the mean.

For SAT score of 1490,

z = (1490-1518)/325 = -0.09

For ACT score of 17.0,

z = (17.0-21.1)/4.8 = -0.854

Therefore, option A and D are true. However, option C is not true since an ACT score of 17.0 has a lower z-score (-0.854) than an SAT score of 1490 (-0.09), indicating that the ACT score is relatively worse than the SAT score. Option B is also true as shown above.

Scores on the SAT Test Have a Mean of 1518