A study of bone density on 5 random women at a hospital produced the following results.
\begin{tabular}{|c|c|c|c|c|c|}
\hline Age & 33 & 37 & 45 & 53 & 61 \\
\hline Bone Density & 345 & 335 & 325 & 320 & 315 \\
\hline
\end{tabular}

Step 2 of 3 : Determine if $r$ is statistically significant at the 0.05 level.

Answer
Yes, the correlation coefficient is statistically significant
No, the correlation coefficient is not statistically significant

Step 1 ：We are given the ages and bone densities of 5 random women at a hospital. The ages are [33, 37, 45, 53, 61] and the corresponding bone densities are [345, 335, 325, 320, 315].

Step 2 ：We need to determine if the correlation coefficient is statistically significant at the 0.05 level. To do this, we first calculate the correlation coefficient.

Step 3 ：The correlation coefficient, denoted as r, is calculated to be -0.9642745893155453.

Step 4 ：We then compare this with the critical value for a two-tailed test at the 0.05 level, which is approximately ±0.878 for a sample size of 5.

Step 5 ：If the absolute value of the correlation coefficient is greater than the critical value, then it is statistically significant.

Step 6 ：The absolute value of our calculated correlation coefficient is greater than the critical value (|-0.964| > 0.878).

Step 7 ：\(\boxed{\text{Therefore, the correlation coefficient is statistically significant at the 0.05 level.}}\)