Question

a study showed that students who spend more time studying for statistics tests tend to achieve better scores on their tests. in fact, the number of hours studied turned out to explain 81% of the observed variation in test scores among the students who participated in the study. what is the value of the correlation between number of hours studied and test score? r = 0.81 r = 0.656 r = 0.9 there is no way to know.

Explanation:

Step1: Recall coefficient - of - determination formula

The coefficient of determination $R^{2}$ represents the proportion of the variance in the dependent variable that is predictable from the independent variable. Given that $R^{2}=0.81$. The correlation coefficient $r$ is related to the coefficient of determination by $R^{2}=r^{2}$.

Step2: Solve for $r$

Since $R^{2}=r^{2}=0.81$, then $r = \pm\sqrt{0.81}=\pm0.9$. Since students who study more tend to have better scores (a positive relationship), we take the positive value of $r$. So $r = 0.9$.

Answer:

$r = 0.9$