Final answer:
The statement that as the sample size increases, the effect of an extreme value on the sample mean becomes smaller is True.
Step-by-step explanation:
The question posed is: As the sample size increases, does the effect of an extreme value on the sample mean become smaller? The answer is A. True. When we are dealing with sample sizes and the central limit theorem, it is important to understand that as the sample size (n) increases, the sample mean will tend to approach the population mean (μ), and thus the effect of an extreme value on the sample mean becomes less significant.
Why does this happen? To delve deeper into the explanation, the central limit theorem states that the distribution of sample means will become increasingly normal as the sample size grows, regardless of the population's distribution shape. As the number surveyed increases, comparisons to the Student's t distribution and the standard normal distribution become more similar.
Moreover, a larger sample size causes the standard deviation of the sampling distribution of the means to decrease. This implies that the sampling variability goes down and each sample mean is more likely to be close to the population mean. With less variability, extreme values have less impact on the overall sample mean.
Additionally, larger sample sizes tend to result in more accurate estimates, leading to narrower confidence intervals, which suggest stronger evidence for estimating the population parameter. While large outliers might significantly affect the sample mean in smaller samples, their impact diminishes as the sample size grows.