All other things being equal, an increase in Sample Size (n) reduces all types of Sampling Errors, including Alpha and Beta Errors and the Margin of Error.
A Sampling "Error" is not a mistake. It is simply the reduction in accuracy to be expected when one makes an estimate based on a portion – a Sample – of the data in Population or Process. There are several types of Sampling Error.
Two types of Sampling Errors are described in terms of their Probabilities:
All three types of Sampling Error are reduced when the Sample Size is increased.
This makes intuitive sense, because a very small Sample is more likely to not be a good representative of the properties of the larger Population or Process. But, the values of Statistics calculated from a much larger Sample are likely to be much closer to the values of the corresponding Population or Process Parameters.
For more on p, see my video P, the p-value. In the future, there will also be videos on Alpha and Beta Error, the Margin of Error, and Confidence Intervals. You can subscribe to the channel to be notified.
Andrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley.