Final answer:
A 99% confidence interval is wider than a 95% confidence interval because it includes a larger portion of the data's distribution, aiming to provide higher certainty that the interval contains the true population parameter.
Step-by-step explanation:
The question pertains to the concept of confidence intervals in statistics, which are used to estimate the range within which a population parameter is likely to lie. A 99% confidence interval is wider than a 95% confidence interval because it aims to capture a larger portion of the data's distribution. The confidence level reflects the degree of certainty we have that the interval contains the population parameter, with higher confidence levels requiring wider intervals due to increased uncertainty.
The wider the confidence interval, the more certain we are that it contains the true population parameter. This is because a wider interval accounts for more of the natural variability in the data. For example, constructing a 98% confidence interval will result in a wider interval compared to a 90% confidence interval because it seeks to include 98% of the possible outcomes, leaving only a 2% chance the true parameter is outside the interval.
It is essential to understand that if we took repeated samples, approximately the stated percentage of these confidence intervals would contain the true population parameter, which is a reflection of the confidence level.