Why is it often easier to start a fitness program than it is to maintain one? A. The motivation at the start of a program is oft
2 answers:
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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 <u>NOT</u> 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
<h2>Answer:</h2><h2 />- <em><u>C) The ACT score of 17.0 is relatively better than the SAT score of 1490:</u></em><em> </em><u>NOT true</u>
To compare scores on different scales or from different groups you need to use a normalized standardized statistic, like the z-score.
Where is the mean of the sample, and
is the standard deviation.
<u>1. Find the z-core for an ACT score of 17.0 </u>
That means that the ACT score of 17.0 is 0.85 standard deviations below the meqan.
<u>2. Find the z-score for an SAT score of 1490</u>
That means that the SAT score of 1490 is 0.09 standard deviations from the mean.
<u>3. Conlusion:</u>
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:
- <em>A) The ACT score of 17.0 is relatively better than the SAT score of 1490</em>: NOT true. ← correct answer
- <em>B) An SAT score of 1490 has a z score of -0.09</em>: TRUE
- <em>C) The SAT score of 1490 is relatively better than ACT score of 17.0</em>: TRUE
- <em>D) An ACT score of 17.0 has a z score of -0.85</em>: TRUE.