When creating a confidence interval, the interval size is influenced by the level of confidence chosen. Here's how it works:
1. Higher confidence levels (such as 95% or 99%) will result in a wider confidence interval. This means that the range of values within which the true population parameter is estimated to lie will be broader. For example, a 95% confidence interval for a mean might be from 10 to 20, while a 99% confidence interval for the same mean might be from 8 to 22.
2. On the other hand, lower confidence levels (like 90% or 80%) will lead to a narrower confidence interval. This indicates a more precise estimate but with less certainty about capturing the true population parameter. For instance, a 90% confidence interval for a mean could be from 12 to 18, whereas an 80% confidence interval for the same mean might be from 13 to 17.
In summary, when it comes to confidence intervals, higher confidence levels result in wider intervals offering more certainty but less precision, while lower confidence levels produce narrower intervals providing greater precision but with reduced certainty.
