As a domain expert in statistics, I can provide a detailed explanation regarding confidence intervals and their percentages. When we talk about confidence intervals, we are discussing a range of values that are likely to contain an unknown population parameter with a certain level of confidence. The level of confidence is expressed as a percentage, and it indicates how certain we can be that the true population parameter lies within the interval.

**Step 1: Understanding Confidence Intervals**

A 95% confidence interval means that if we were to take many samples from the same population and calculate a confidence interval from each sample, then 95% of those intervals would contain the true population parameter. Similarly, a 99% confidence interval would contain the true population parameter in 99% of the samples.

The width of a confidence interval is influenced by several factors, including the level of confidence, the sample size, and the variability within the data. When we increase the level of confidence from 95% to 99%, we are stating that we want to be more certain that the interval contains the true population parameter. To achieve this higher level of certainty, the interval must be wider to account for more potential variability.

The Width of Confidence Intervals

The statement that a 99% confidence interval is more accurate than a 95% confidence interval is somewhat misleading. Accuracy in this context refers to the precision of the estimate, not the correctness. A higher confidence level does not mean the interval is more accurate in the sense of being closer to the true value; rather, it means that the interval is constructed to be more inclusive, capturing a wider range of possible values.

Statistical Precision vs. Accuracy

The precision of an estimate is related to the width of the confidence interval. A narrower interval suggests a more precise estimate because it indicates that the sample data are more consistent with each other. However, this does not necessarily mean it is more accurate. The accuracy of an estimate is about how close the estimate is to the true value, which is not directly related to the width of the confidence interval.

Factors Affecting the Width

The width of a confidence interval is also affected by the sample size (n). As the sample size increases, the variability within the sample decreases, which leads to a narrower confidence interval for the same level of confidence. This is because larger samples provide more information about the population, allowing for a more precise estimate.

**Implications for Research and Decision Making**

In practice, the choice between a 95% and a 99% confidence interval depends on the context and the consequences of being wrong. For example, in life-critical applications such as medical testing, a 99% confidence interval might be preferred to minimize the risk of missing the true parameter. In contrast, for less critical applications, a 95% confidence interval might be sufficient to make decisions.

Conclusion

In summary, a 99% confidence interval is wider than a 95% confidence interval because it covers a greater range of values to achieve a higher level of confidence. However, this does not imply that the 99% interval is more accurate in terms of being closer to the true population parameter. The choice of confidence level should be based on the specific requirements of the study or decision-making process.

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Apparently a narrow confidence interval implies that there is a smaller chance of obtaining an observation within that interval, therefore, our accuracy is higher. Also a 95% confidence interval is narrower than a 99% confidence interval which is wider. The 99% confidence interval is more accurate than the 95%.Sep 28, 2011read more >>