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A survey of 1,026 people asked about what they would do with an unexpected cash gift. Forty-seven percent responded that they would pay off debts. a. With $95 \%$ confidence, what is the margin of error?
Note: Round final answer to 3 decimal places. Margin of error $\square$ b. Construct the $95 \%$ confidence interval for the population proportion of people who would pay off debts with an unexpected cash gift. Note: Round final answers to 3 decimal places. \begin{tabular}{|l|l|} \hline Lower limit & \\ \hline Upper limit & \\ \hline \end{tabular}