. As the sample size increases
The confidence interval also increases (gets larger)
The confidence interval decreases (gets smaller)
The confidence interval stays the same
The population mean increases.
With larger samples, the confidence interval decreases.
As the sample size increases, the confidence interval decreases (gets smaller).
To understand why this happens, let's first understand what a confidence interval is. A confidence interval is a range of values within which we estimate a population parameter, such as the population mean. It is based on a sample taken from that population.
When we calculate a confidence interval, we use a specified level of confidence, usually expressed as a percentage (e.g., 95% confidence interval). This represents our confidence in the accuracy of the estimate.
When the sample size increases, we have more data points to work with. This means that our estimate of the population mean becomes more precise and accurate. As a result, the range of values within which we expect the true population mean to fall narrows. In other words, the confidence interval becomes smaller.
So, as the sample size increases, the confidence interval decreases in size because our estimate becomes more precise due to the increased amount of data.