Final answer:
Larger sample sizes result in narrower control limits for a process, due to a decrease in error bound and reduction in sampling variability, which enhances estimate precision and reliability.
Step-by-step explanation:
Larger sample sizes tend to lead to narrower control limits on a process. This occurs because as you increase the sample size, the error bound decreases, leading to more precise estimates of the population parameter. As the sample size grows, the variability between sample statistics reduces, enhancing the reliability of the statistic, and thereby leading to narrower control limits.
The Central Limit Theorem supports this by stating that the larger the sample, the closer the sampling distribution of the mean becomes to a normal distribution. Furthermore, larger sample sizes are less prone to the effects of sampling variability and more closely model the population from which they are drawn. However, it is imperative to consider that increasing the sample size does have practical limitations and requires balancing resource constraints and the benefits of increased precision.