Question

Scores on required state math tests along with school attendance (days) were collected for 72 sixth-grade students. The standardized z-scores of the test results and those of the students' attendance days were calculated and the pairs multiplied together. The sum of these 72 products was 57.15. Based on this sum, what can you conclude about the correlation between math scores and days of attendance?

Answer 1

The sum of the z-score products indicates a strong positive correlation between math scores and days of attendance for sixth-grade students; the calculated correlation coefficient is approximately 0.79.

Step-by-step explanation:

The sum of the products of the standardized z-scores for math test results and attendance days for 72 sixth-grade students is 57.15. To understand the correlation between math scores and days of attendance based on this sum, one must turn to the formula for the Pearson correlation coefficient (r), which, when using z-scores, is the sum of the product of paired z-scores divided by the number of pairs. Here, it seems we have been provided the numerator of this calculation. To get the correlation coefficient, we would divide 57.15 by 72, the number of pairs, which equals approximately 0.79. This indicates a strong positive correlation between math test scores and days of attendance. In other words, there is a tendency that students with more days of attendance tend to have higher math test scores.