1. **State the problem:** We are given a table of data with two variables: Minutes and Errors. We need to find the correlation coefficient $r$ that measures the strength and direction of the linear relationship between these two variables. 2. **Recall the formula for the correlation coefficient $r$:** $$r = \frac{n\sum xy - \sum x \sum y}{\sqrt{(n\sum x^2 - (\sum x)^2)(n\sum y^2 - (\sum y)^2)}}$$ where $x$ and $y$ are the variables, and $n$ is the number of data points. 3. **List the data points:** Minutes ($x$): 2, 4, 7, 8, 9 Errors ($y$): 30, 20, 15, 24, 13 4. **Calculate the necessary sums:** $$\sum x = 2 + 4 + 7 + 8 + 9 = 30$$ $$\sum y = 30 + 20 + 15 + 24 + 13 = 102$$ $$\sum xy = (2)(30) + (4)(20) + (7)(15) + (8)(24) + (9)(13) = 60 + 80 + 105 + 192 + 117 = 554$$ $$\sum x^2 = 2^2 + 4^2 + 7^2 + 8^2 + 9^2 = 4 + 16 + 49 + 64 + 81 = 214$$ $$\sum y^2 = 30^2 + 20^2 + 15^2 + 24^2 + 13^2 = 900 + 400 + 225 + 576 + 169 = 2270$$ 5. **Plug values into the formula:** $$r = \frac{5(554) - (30)(102)}{\sqrt{[5(214) - 30^2][5(2270) - 102^2]}}$$ 6. **Simplify numerator:** $$5(554) = 2770$$ $$(30)(102) = 3060$$ $$\text{Numerator} = 2770 - 3060 = -290$$ 7. **Simplify denominator parts:** $$5(214) = 1070$$ $$30^2 = 900$$ $$5(2270) = 11350$$ $$102^2 = 10404$$ 8. **Calculate denominator:** $$\sqrt{(1070 - 900)(11350 - 10404)} = \sqrt{170 \times 946} = \sqrt{160820}$$ 9. **Calculate square root:** $$\sqrt{160820} \approx 400.99$$ 10. **Calculate $r$:** $$r = \frac{-290}{400.99} \approx -0.723$$ **Final answer:** The correlation coefficient $r$ rounded to the nearest hundredth is **$-0.72$**.