Astatistics student computes the correlation between two variables in her spreadsheet, and finds r = 0.06. she decides to conclude there is no relationship between the variables. was she correct?

She could be correct; however, we don't have enough information to determine if she was correct.

The value, r = 0.06, shows a very weak linear relationship (but only measures linear relationships; so the relationship could be something else.
We need to see the data plotted and graphed to make a determination.