Final answer:
The standard deviation of the sampling distribution decreases as the sample size increases, reflecting less variation among the sample means. This concept is related to the standard error of the mean, which grows smaller with larger samples, yielding more precise estimates of the population mean.
Step-by-step explanation:
As the sample size increases, the standard deviation of the sampling distribution typically decreases. This is because as you take larger samples from a population, the sample means will tend to be closer together, meaning there is less variation among them. This is reflected in the concept of the standard error of the mean, which is the standard deviation of the sampling distribution of the mean. The standard error of the mean decreases as the sample size increases, following the formula σ/√n, where σ is the population standard deviation and n is the sample size.
According to the Central Limit Theorem, as the sample size grows, the distribution of the sample means will approach a normal distribution. This normal distribution will have a mean equal to the population mean and a standard deviation called the standard error, which gets smaller as the sample size increases. Hence, when considering the effect of changing the sample size, an increased sample size results in a narrower confidence interval, which indicates a more precise estimate of the population mean.