The following data gives the number of hours 7 students spent studying and their corresponding grades on their midterm exams.
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline Hours Spent Studying & 0.5 & 1.5 & 2.5 & 3 & 3.5 & 4 & 4.5 \\
\hline Midterm Grades & 72 & 78 & 81 & 87 & 90 & 96 & 99 \\
\hline
\end{tabular}
Step 2 of 3: Determine if $r$ is statistically significant at the 0.05 level.
Answer
4 Points

Step 1 ：The given data represents the number of hours 7 students spent studying and their corresponding grades on their midterm exams. The hours spent studying are [0.5, 1.5, 2.5, 3, 3.5, 4, 4.5] and the corresponding midterm grades are [72, 78, 81, 87, 90, 96, 99].

Step 2 ：We are asked to determine if the correlation coefficient, r, is statistically significant at the 0.05 level. This involves calculating the correlation coefficient from the given data and then comparing it to the critical value for a two-tailed test at the 0.05 level with degrees of freedom equal to n-2, where n is the number of pairs of data.

Step 3 ：The correlation coefficient, r, measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.

Step 4 ：The critical value for a two-tailed test at the 0.05 level with degrees of freedom equal to n-2 can be found in a statistical table. If the absolute value of r is greater than the critical value, then r is statistically significant at the 0.05 level.

Step 5 ：The correlation coefficient, r, is approximately 0.99, which indicates a very strong positive linear relationship between the number of hours spent studying and the midterm grades. However, the absolute value of r is not greater than the critical value for a two-tailed test at the 0.05 level with degrees of freedom equal to 5, which is approximately 2.57.

Step 6 ：Final Answer: The correlation coefficient, r, is not statistically significant at the 0.05 level. Therefore, we cannot reject the null hypothesis that there is no linear relationship between the number of hours spent studying and the midterm grades. \(\boxed{\text{False}}\).