A research firm has found that 39% of U.S. adults in the over-$75,000 income category work at least 51 hours per week. Assuming this was a simple random sample of 500 adults in this income group, construct and interpret the 95% and 99% confidence intervals for the proportion who work at least 51 hours per week. For each of the confidence intervals, identify and explain the maximum likely error in the study.