Assume a significance level of $\alpha=0.05$ and use the given information to complete parts (a) and (b) below.
Original claim: Less than $59 \%$ of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of 0.0081.
a. State a conclusion about the null hypothesis. (Reject $\mathrm{H}_{0}$ or fail to reject $\mathrm{H}_{0}$.) Choose the correct answer below.
A. Fail to reject $\mathrm{H}_{0}$ because the $P$-value is greater than $\alpha$.
B. Reject $\mathrm{H}_{0}$ because the P-value is less than or equal to $\alpha$.
C. Fail to reject $\mathrm{H}_{0}$ because the P-value is less than or equal to $\alpha$.
D. Reject $\mathrm{H}_{0}$ because the $\mathrm{P}$-value is greater than $\alpha$.
b. Without using technical terms, state a final conclusion that addresses the original claim. Which of the following is the correct conclusion?
A. The percentage of adults that would erase all of their personal information online if they could is more than or equal to $59 \%$.
B. The percentage of adults that would erase all of their personal information online if they could is less than $59 \%$.
C. There is not 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 $59 \%$.
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 $59 \%$.
Answer
\(\boxed{\text{Final Answer: (a) B, (b) D}}\)
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 ：\(\boxed{\text{Final Answer: (a) B, (b) D}}\)
