An instructor decided to determine if there was a correlation between how close to the front of the class students sat and the students’ final grades in the class (in terms of number of points). The report of the results included this: "r = -0.23, n = 30, p = 0.0221." From this alone, which of the following is the most accurate statement you could make?

Group of answer choices:
1. The closer the students sat to the front of the class, the higher were their grades.
2. The closer the students sat to the front of the class, the lower were their grades.
3. There was not a statistically significant correlation between where students sat and the final grades.

Question

12-04-2025
Mathematics

High School

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An instructor decided to determine if there was a correlation between how close to the front of the class students sat and the students’ final grades in the class (in terms of number of points). The report of the results included this: "r = -0.23, n = 30, p = 0.0221." From this alone, which of the following is the most accurate statement you could make?

Group of answer choices:
1. The closer the students sat to the front of the class, the higher were their grades.
2. The closer the students sat to the front of the class, the lower were their grades.
3. There was not a statistically significant correlation between where students sat and the final grades.

Answer :

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OliviaMariThompson OliviaMariThompson · Answer 1 · 2025-05-14T04:12:18-04:00

To understand the instructor's analysis, we need to look at the statistics terms given in the report:

Correlation Coefficient (r = -0.23): This number represents the strength and direction of a linear relationship between two variables. A value of -0.23 indicates a weak negative correlation. This means that as students' seating in the classroom approaches the front, their grades tend to decrease slightly. However, the correlation is not strong, suggesting that many other factors might be influencing the grades.
Sample Size (n = 30): This indicates the number of participants in the study. The sample size can influence the statistical significance of the results. In this case, the data comes from 30 students, which is a moderate sample size for such a correlation study.
P-Value (p = 0.0221): The p-value tells us about the statistical significance of the results. A p-value less than 0.05 is typically considered statistically significant. Here, p = 0.0221, which means the result is statistically significant, and the observed correlation is unlikely to have occurred by random chance.

Given these points, the correct statement is:

The closer the students sat to the front of the class, the lower were their grades.

This conclusion, however, should be taken cautiously due to the weak nature of the correlation (-0.23). It's important to note that correlation does not imply causation. There may be other variables affecting student grades in this scenario.