The margin of error (increases or decreases?) with an increased sample size and (increases or decreases?) with an increase in confidence level.

Increased Sample Size: When the sample size increases, the standard error of the sample mean decreases. As a result, the margin of error, which is directly proportional to the standard error, decreases. With a larger sample size, the estimate of the population parameter becomes more precise, leading to a smaller margin of error. Increase in Confidence Level: When the confidence level increases, the z-score corresponding to that confidence level also increases. Since the margin of error is proportional to the z-score and the standard error, an increase in the z-score results in a larger margin of error. This means that with a higher confidence level, we're allowing for a greater range of values around the sample estimate, leading to a larger margin of error. In summary, an increased sample size decreases the margin of error, while an increase in confidence level increases the margin of error.