Final answer:
Increasing the sample size leads to narrower confidence intervals as the estimator becomes more precise with larger samples. The standard error diminishes with larger samples, resulting in tighter intervals that are more representative of the population parameter. Option 3
Step-by-step explanation:
When the size of samples increases, the confidence interval band becomes narrower. This happens because a larger sample size reduces the standard error, which is a measure of the uncertainty or variability in the sample estimate.
As the standard error decreases, the interval within which we can say we are confident the true population parameter lies becomes smaller. Therefore, a larger sample provides more information and increases the precision of our estimate of the population parameter, resulting in a tighter confidence interval.
To further clarify, the confidence interval (CI) is a range of values, derived from the sample data, that is likely to cover the true population parameter. As the sample size grows, the estimations from the sample become more representative of the whole population, hence reducing the need for a wide interval to ensure the population parameter is included. Option 3