How does an increase in sample size affect the distribution of the sample mean?

An increase in sample size has a significant effect on the distribution of the sample mean, specifically leading it to approximate a normal distribution. This phenomenon is supported by the Central Limit Theorem, which states that regardless of the population’s original distribution, if the sample size is sufficiently large (commonly n ≥ 30 is used as a rule of thumb), the distribution of the sample means will tend to be normal.

This means that as the sample size increases, the means of these samples will cluster around the true population mean with less variability, resulting in a tighter and more symmetric shape that resembles a normal distribution. This is crucial in statistics as it allows for the application of normal probability techniques even without the need to know the underlying population distribution, thereby enhancing our ability to conduct various statistical tests and make inferences about the population.

In contrast, other options propose incorrect effects of increasing sample size, such as implying that the distribution becomes skewed, that variability increases or that accuracy decreases, all of which do not align with the principles established by the Central Limit Theorem and the understanding of statistical distributions.