Final answer:
Olivia's data showing a correlation coefficient of 0.52 indicates a weak positive correlation between the number of math homework problems and the time it takes to complete them, making statement B correct.
Step-by-step explanation:
The correlation coefficient that Olivia calculated for her math homework problems is 0.52. This number falls between 0 and 1, indicating that there is a positive correlation between the number of math homework problems and the time it takes to complete them. However, since the coefficient is closer to 0 than to 1, we can conclude that it is a weak positive correlation. This means that, generally, as the number of math problems increases, so does the time it takes to complete them, but the relationship isn't strong enough to be considered highly predictive.
Therefore, the statement B is true: There is a weak positive correlation between the number of math homework problems and the time it takes Olivia to complete them. The other statements are false: Statement A is incorrect because the correlation is not strong enough; Statement C is incorrect because the correlation is positive, not negative; and Statement D is incorrect because a correlation coefficient of 0.52 indicates that there is indeed some correlation, albeit a weak one.