T/F: There is a trade-off between the confidence level and the margin of error. To obtain a smaller margin of error from the same data, you must be willing to accept lower confidence.
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True. There is an inverse relationship between the confidence level and the margin of error. Raising the confidence level (say, from 90% to 95%) will increase the margin of error, all else being equal. Likewise, reducing the margin of error would require a lower confidence level. This is because a higher confidence level means that you are more certain that the results reflect the true population parameter, which necessitates a larger sample size (which lowers the margin of error). On the other hand, a higher margin of error implies less precision in the estimate, which could admit more error in the results, thereby reducing the level of confidence.
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