Which confidence interval is likely to more accurately contain the true population mean?

Which confidence interval is likely to more accurately contain the true population mean?

• A. A 90% confidence interval (CI)
• B. A 95% CI
• C. A 99% CI
• D. All of the above

Answer: (C)

The choice of a 99% confidence interval indicates a higher degree of certainty that the interval will contain the true population mean compared to lower confidence levels. This is due to the fact that as the confidence level increases, the interval becomes wider to account for greater variability and uncertainty. A 99% confidence interval captures a larger portion of the distribution, thereby enhancing the likelihood that it includes the true population mean. Choosing a higher confidence level, such as 99%, implies that there is only a 1% chance of the interval not containing the true population mean, as opposed to a 10% chance for a 90% confidence interval or a 5% chance for a 95% confidence interval. Therefore, when seeking the most accurate representation of the population mean within a confidence interval framework, a 99% confidence interval is designed to be more reliable in achieving this goal, making it the best choice. While lower confidence intervals can still provide valuable insights, they inherently come with a higher risk of excluding the true mean, which is not the case with a 99% CI.

The choice of a 99% confidence interval indicates a higher degree of certainty that the interval will contain the true population mean compared to lower confidence levels. This is due to the fact that as the confidence level increases, the interval becomes wider to account for greater variability and uncertainty. A 99% confidence interval captures a larger portion of the distribution, thereby enhancing the likelihood that it includes the true population mean.

Choosing a higher confidence level, such as 99%, implies that there is only a 1% chance of the interval not containing the true population mean, as opposed to a 10% chance for a 90% confidence interval or a 5% chance for a 95% confidence interval. Therefore, when seeking the most accurate representation of the population mean within a confidence interval framework, a 99% confidence interval is designed to be more reliable in achieving this goal, making it the best choice.

While lower confidence intervals can still provide valuable insights, they inherently come with a higher risk of excluding the true mean, which is not the case with a 99% CI.