As a statistical expert with a strong background in data analysis and interpretation, I can provide a comprehensive explanation regarding the concept of confidence intervals and how they relate to confidence levels.

Confidence intervals are a fundamental concept in statistical analysis, providing a range within which we can be confident that the true value of a population parameter lies. The level of confidence, often expressed as a percentage, indicates the degree of certainty we have about the interval containing the true value. It is important to note that the confidence level is not the same as the probability that the interval contains the true value, but rather the proportion of all possible intervals that would contain the true value if we were to repeat the sampling process an infinite number of times.

The width of a confidence interval is influenced by several factors, including the confidence level, the sample size, the variability within the data, and the standard error of the estimate. When we talk about the width of a confidence interval, we are typically referring to the margin of error, which is the range that is added and subtracted from the sample statistic to create the interval.

Now, let's address the question of whether a 95% confidence interval is wider than a 90% confidence interval. The answer is generally yes, a 95% confidence interval is wider than a 90% confidence interval. This is because a higher confidence level implies a larger margin of error is needed to achieve that level of confidence. In other words, to be more certain (95% instead of 90%) that the interval contains the true value, we need to increase the range of values that we are considering.

The reference content provided suggests that a 99% confidence interval would be wider than a 95% confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent), and a 90% confidence interval would be narrower (plus or minus 2.5 percent, for example). This is a correct illustration of the principle that higher confidence levels require wider intervals to maintain the same level of certainty about the parameter's location within the interval.

To further illustrate this, let's consider a hypothetical example. Suppose we are estimating the mean height of a population of adults. If we calculate a 90% confidence interval based on a sample, we might find that the interval is, say, between 170 cm and 175 cm. To increase our confidence to 95%, we would need to add more to both ends of the interval to account for the increased certainty we want to achieve. This could result in a new interval of, for instance, 168 cm to 178 cm.

In summary, the width of a confidence interval is directly related to the confidence level. As the confidence level increases, the interval becomes wider to encompass a greater range of values that could potentially contain the true population parameter. This is a fundamental principle in statistical analysis and is essential for understanding how to interpret and use confidence intervals in practice.

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A 99 percent confidence interval would be wider than a 95 percent confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent). A 90 percent confidence interval would be narrower (plus or minus 2.5 percent, for example).read more >>