You plan to construct a confidence interval for the mean \muμ of a Normal population with (known) standard deviation \sigmaσ. Which of the following will reduce the size of the margin of error? Group of answer choices Use a lower level of confidence. Increase the sample size. Reduce \sigma σ . All of the answers are correct.

All of the answers are correct. Each of the options provided will lead to a reduction in the size of the margin of error for the confidence interval.

1. Use a lower level of confidence: A lower level of confidence means that there is a smaller probability that the confidence interval will contain the true population mean \(\mu\). Since the level of confidence (such as 90%, 95%, or 99%) corresponds to the width of the confidence interval, lower confidence levels result in narrower intervals and therefore smaller margins of error.

2. Increase the sample size: A larger sample size provides more information about the population and results in a smaller standard error of the mean. Since the margin of error is directly proportional to the standard error, an increased sample size leads to a smaller margin of error.

3. Reduce \(\sigma\): The standard deviation \(\sigma\) is a measure of the amount of variation or dispersion in the data. The margin of error is partially determined by the standard deviation; a smaller standard deviation means there is less variability in the data, which results in a smaller margin of error.