If a student's high school GPA is 2.5 standard deviations above the mean, what college GPA can we expect based on a correlation coefficient of 0.560?

To determine the expected college GPA based on a student's high school GPA that is 2.5 standard deviations above the mean, we can use the concept of the correlation coefficient. The correlation coefficient, in this case, is 0.560, indicating a moderate positive relationship between high school GPA and college GPA.

When a student's high school GPA is 2.5 standard deviations above the mean, we can use the formula for the predicted change in the college GPA, which can be expressed as the correlation coefficient multiplied by the number of standard deviations from the mean in high school GPA. Specifically, if a GPA is 2.5 standard deviations above the mean, to find the equivalent change in college GPA, we multiply this distance by the correlation coefficient.

So, the expected change in college GPA would be:

Expected change = Correlation coefficient * Standard deviations above the mean

= 0.560 * 2.5

Calculating this gives us:

Expected change = 1.4

Thus, we can confidently expect the college GPA to be approximately 1.4 standard deviations above the mean for a student with a high school GPA that is 2.5 standard deviations above the mean. This understanding is reinforced by the moderate positive correlation between