Question
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For a group of students in a statistics class, the scatter diagram compares their test scores ( \( y \) ) and the number of pencils they have ( \( x \). State whether there is no correlation or a negative correlation between the \( x \) and \( y \) variables. If there is a correlation, state whether it is most likely due to coincidence, a common underlying cause, or a direct cause. A. Negative correlation; direct cause B. Negative correlation; coincidence C. No correlation D. Negative correlation; common underlying cause

Ask by Daniel Mitchell. in the United States
Mar 09,2025

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Answer

There is a negative correlation between the number of pencils and test scores, and this correlation is most likely due to a common underlying cause.

Solution

1. The scatter diagram shows a negative relationship between the \( x \) variable (number of pencils) and the \( y \) variable (test scores). This means that as the number of pencils increases, the test scores tend to decrease. 2. However, it is important to consider whether this negative correlation implies a direct cause-and-effect relationship. In many cases where variables appear to be correlated, there might be a third factor influencing both. For example, an underlying factor such as the students’ organization or study habits might be influencing both the number of pencils they carry and their performance on tests. 3. Since having many pencils does not directly cause low test scores (nor do low test scores cause a student to carry more pencils), the negative correlation is most likely due to a common underlying cause rather than a direct cause. Thus, the correct answer is: D. Negative correlation; common underlying cause.

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Beyond the Answer

It sounds like you might be observing a negative correlation, implying that as the number of pencils increases, test scores tend to decrease. This could be interpreted as a sign that students with more pencils might be distracted or less focused on studying, but it’s also essential to consider other factors at play. Often, correlations can be misleading! Just because you see a pattern doesn’t mean one factor is causing the other. In this case, it might simply be coincidence or a sign of other variables affecting study habits and performance, like time spent preparing for tests rather than playing with pencils!

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