Question

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 explain

Answer 1

The complete question is:

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?

Options:

A) The ACT score of 17.0 is relatively better than the SAT score of 1490

B) An SAT score of 1490 has a z score of -0.09

C) The SAT score of 1490 is relatively better than ACT score of 17.0

D) An ACT score of 17.0 has a z score of -0.85

Answer:

• C) The ACT score of 17.0 is relatively better than the SAT score of 1490:        NOT true

Explanation:

To compare scores on different scales or from different groups you need to use a normalized standardized statistic, like the z-score.

          $z-score=(score-\mu)/\sigma$

Where $\mu$ is the mean of the sample, and $\sigma$ is the standard deviation.

1. Find the z-core for an ACT score of 17.0

          $z-score=(score-\mu)/\sigma\\ \\ z-score=(17.0-21.1)/4.8\\ \\ z-score=-0.85$

That means that the ACT score of 17.0 is 0.85 standard deviations below the meqan.

2. Find the z-score for an SAT score of 1490

            $z-score=(score-\mu)/\sigma\\ \\ z-score=(1490-1518)/325\\ \\ z-score=-0.086\approx -0.09$

That means that the SAT score of 1490 is 0.09 standard deviations from the mean.

3. Conlusion:

Since the z-score of the SAT score of 1490 is greater than the z-score of the ACT of 17.0, the SAT score of 1490 is relatively better than the aCT score of 17.0.

As for the answer choices:

• A) The ACT score of 17.0 is relatively better than the SAT score of 1490: NOT true. ← correct answer

• B) An SAT score of 1490 has a z score of -0.09: TRUE

• C) The SAT score of 1490 is relatively better than ACT score of 17.0: TRUE

• D) An ACT score of 17.0 has a z score of -0.85: TRUE.