How would an increase in sample size affect the sampling distribution?

An increase in sample size has a significant impact on the properties of the sampling distribution, particularly in terms of the shape, spread, and central tendency. According to the Central Limit Theorem, as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution from which the samples are drawn. This convergence towards normality is especially pronounced with larger sample sizes, typically considered to be 30 or more.

This property is crucial in statistical analysis as it allows researchers to apply inferential statistics techniques that rely on the assumption of normality. By increasing the sample size, one can also expect the standard error of the mean (the standard deviation of the sampling distribution) to decrease, making estimates of the population parameter more precise.

The other options do not accurately reflect the underlying principles of statistics: the shape of the distribution does change as the sample size increases; it would not flatten but rather exhibit tighter clustering around the mean, and while the mean is also influenced by sample size, the primary effect is on the distribution's shape and spread rather than just the mean itself. Hence, an increase in sample size indeed makes the curve approach normality, which is why that answer is correct.