Step 1 :Given that the significance level, \(\alpha\), is 0.05 and the P-value is 0.0081.
Step 2 :Since the P-value is less than the significance level, we reject the null hypothesis. So, the answer to part (a) is B. Reject \(\mathrm{H}_{0}\) because the P-value is less than or equal to \(\alpha\).
Step 3 :Since we rejected the null hypothesis, this means that we have sufficient evidence to support the claim that less than 59% of adults would erase all of their personal information online if they could.
Step 4 :So, the answer to part (b) is D. There is sufficient evidence to support the claim that the percentage of adults that would erase all of their personal information online if they could is less than 59%.
Step 5 :\(\boxed{\text{Final Answer: (a) B, (b) D}}\)