How can one achieve a high confidence level while maintaining a small margin of error?

To achieve a high confidence level while maintaining a small margin of error, increasing the sample size is an effective strategy. When the sample size is larger, the estimates become more precise, which reduces the margin of error. This is rooted in the statistical principle that larger samples tend to better reflect the characteristics of the population due to the law of large numbers. As the sample size increases, the variability of the sample mean decreases, which leads to a tighter confidence interval around the true population parameter.

Additionally, a larger sample size allows for a higher degree of accuracy in estimating the population parameters while still achieving a desired level of confidence. This means that you can say with more assurance (higher confidence level) that your estimate is close to the true population value while ensuring that the margin of error remains small.

The other options, while potentially leading to adjustments in confidence intervals, do not directly relate to achieving both a high confidence level and a small margin of error simultaneously in the way increasing the sample size does. Decreasing the confidence level would reduce the confidence but not maintain a small margin of error effectively. Reducing the population standard deviation might be situational and not under control, and using a smaller planning value of p applies to specific contexts but does not address the overall