Final answer:
The 99% confidence interval is wider than the 95% confidence interval because it provides a higher degree of certainty, encompassing more of the population distribution to maintain the confidence level.
Step-by-step explanation:
The 99% confidence interval is wider than the 95% confidence interval. The 99% confidence interval ranges from 75 to 89, which is a 14-unit interval. In contrast, the 95% confidence interval ranges from 77 to 87, which is a 10-unit interval. The reason a 99% confidence interval is wider is that it aims to capture the true population mean μ with a higher degree of certainty. To achieve this higher confidence level, the interval must be extended to include more of the population distribution, thereby increasing the range from the lower bound to the upper bound.
A larger confidence level results in a larger interval because it accounts for more of the distribution, requiring broader bounds to maintain the stated level of confidence.The 99% confidence interval is larger because it includes a greater percentage of the distribution. The 95% confidence interval excludes 5% of the distribution, while the 99% confidence interval excludes only 1% of the distribution. Therefore, the 99% confidence interval is wider because it needs to encompass more possible values of the population mean.