Final answer:
Decreasing the confidence level of a confidence interval leads to a narrower interval with a smaller error bound, reflecting a higher risk that the interval does not contain the true population parameter.
Step-by-step explanation:
When you decrease the confidence level for a given confidence interval, the error bound decreases, resulting in a narrower confidence interval. This means that the interval in which you are confident that the true population parameter will fall is smaller. As the confidence level is decreased, there is less need for area under the normal curve to capture the true population mean. It is important to note that a lower confidence level also implies a lower guarantee of capturing the true population parameter in the interval.
For example, going from a 99% confidence level to a 90% confidence level means we are accepting a higher risk that our interval will not contain the true mean, but as a trade-off, we get a narrower interval, which gives a more precise estimate of the population parameter.