provided in the table to complete parts a) throuph d) \begin{tabular}{|c|c|c|c|c|c|c|} \hline Carbotiydrates (grarns) & 7.5 & 9 & 1 & 2 & 7 & 7 \\ \hline Energy (kilocalories) & 23 & 33 & 24 & 13 & 22 & 32 \\ \hline \end{tabular} (i) Click the icon to view the correlation coefficient, $r$, for varbous values of $n$ and $a$ a) Doternine the correlation coefficient between the amount of carbohydrates and the energy provided The correlation coefficient between the amount of carbohydrates and the energv provided is $r=\square$ (Type an integer or decimal rounded to three decimal places as needed) b) Determine whether a correlation exists at $\alpha=0.05$ Choose the correct answer below A linear correlation does not exist. A linear correlation exists

Step 1 ：The correlation coefficient, often denoted by r, measures the strength and direction of a linear relationship between two variables. In this case, we are asked to find the correlation coefficient between the amount of carbohydrates and the energy provided.

Step 2 ：Given the carbohydrates values as [7.5, 9, 1, 2, 7, 7] and energy values as [23, 33, 24, 13, 22, 32].

Step 3 ：Calculate the correlation coefficient, r, between these two sets of values.

Step 4 ：The calculated correlation coefficient, r, is approximately 0.641. This value is between 0.5 and 1, indicating a moderate positive correlation between the amount of carbohydrates and the energy provided.

Step 5 ：This means that as the amount of carbohydrates increases, the energy provided also tends to increase. However, this is not a strong correlation, so there may be other factors at play.

Step 6 ：Final Answer: The correlation coefficient between the amount of carbohydrates and the energy provided is \( \boxed{0.641} \).