As a domain expert in statistics, I can tell you that a 95% confidence limit is a fundamental concept in inferential statistics that describes the range within which we expect the true population parameter to lie with a certain level of confidence. It is derived from the confidence interval, which is a range that includes the population parameter of interest, such as the mean, proportion, or difference between groups.

When statisticians talk about a 95% confidence interval, they mean that if they were to take many samples from the same population and calculate the confidence interval for each sample, then 95% of these intervals would contain the true population parameter. It's important to note that this does not mean that there is a 95% chance the parameter is within the calculated interval for a single sample; rather, it's the proportion of intervals that would contain the parameter if the process were repeated many times.

The calculation of a confidence interval typically involves the following steps:


1. Estimation of the Parameter: First, you estimate the parameter of interest from your sample data. For instance, if you're interested in the mean height of a population, you would calculate the mean height of your sample.


2. Margin of Error: Next, you determine the margin of error (also known as the standard error), which measures the amount of error in the estimation of the parameter. This is often calculated using the standard deviation of the sample and the sample size.


3. Critical Value: You then identify a critical value from a statistical distribution, such as the normal distribution or the t-distribution, that corresponds to the desired level of confidence. For a 95% confidence level, the critical value is typically around 1.96 for a normal distribution.


4. Calculation of the Interval: Finally, you calculate the confidence interval by adding and subtracting the margin of error multiplied by the critical value to the estimated parameter.

Here's the formula for a confidence interval for a mean (μ):
\[ \text{Confidence Interval} = \bar{x} \pm (t_{\text{critical}} \times \text{SE of } \bar{x}) \]
where \( \bar{x} \) is the sample mean, \( t_{\text{critical}} \) is the critical t-value for the given confidence level and degrees of freedom, and SE of \( \bar{x} \) is the standard error of the mean.

It's also worth mentioning that the choice of the confidence level (e.g., 90%, 95%, 99%) depends on how certain you want to be about including the true population parameter. A higher confidence level provides a wider interval, indicating a greater level of certainty but at the cost of precision.

Now, let's move on to the translation.

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Confidence limits are the numbers at the upper and lower end of a confidence interval; for example, if your mean is 7.4 with confidence limits of 5.4 and 9.4, your confidence interval is 5.4 to 9.4. Most people use 95% confidence limits, although you could use other values.Jul 20, 2015read more >>