As sample size increases, what happens to the standard error of $M$?

Hint: Standard error can be defined as the evaluation of the accuracy of any estimation made with the regression line. It is represented as SE and in statistics the sample refers to the data which is gathered for the particular group. The standard error is an important statistical measure which is related to the standard deviation.

Complete step by step solution:
The standard error is an important statistical measure which is related to the standard deviation. It tells the way sample means determine the true population means. A population can be defined as a whole group from which the data has been gathered. When there is a large standard error it indicates that there are various changes in the population whereas when there is a small standard error it implies that the population is in a uniform shape.

The precision of a sample that represents a population can be identified with the help of standard error equations. The sample mean can be calculated from the given population by using the formula
$SE = \dfrac{s}{{\sqrt n }}$
Where $s$ is the standard deviation and $n$ is the number of observations.So, if we increase the number of observations or sample size the standard error of mean decreases as standard error of mean is inversely proportional to the square root of $n$.

Hence, standard error of $M$ decreases with the increase in sample size.

Note: Standard error of mean, also known as standard deviation of mean is a method used to calculate the standard deviation of the sampling distribution. It is also denoted by SEM. The standard error of the mean can be defined as the way the mean changes with different experiments when we are measuring a similar quantity. The formula of standard error states that the larger the sample size, the smaller the standard error.