Final answer:
The margin of error is a function of the standard deviation, sample size, and the confidence level's critical value; increasing the sample size decreases the margin of error, while decreasing it has the opposite effect.
Step-by-step explanation:
The margin of error in statistics is a measure of the range within which we can expect the true population parameter to lie, considering a certain confidence level.
This value depends upon the standard deviation, the sample size (n), and the critical value associated with the desired confidence level.
When the sample size (n) increases, the margin of error decreases, making the confidence interval narrower. Conversely, if we decrease the sample size, the margin of error increases, resulting in a wider confidence interval. This relationship shows that as more data is collected (with a larger n), our estimates become more precise.
For example, with a confidence level of 95% (Z=1.96), we can calculate the EBM (error bound of mean) by applying the formula EBM = Z * (σ/√n) where σ is the standard deviation.