What Confidence interval is
A confidence interval is a type of interval estimate of a population parameter and is used to indicate the reliability of an estimate. It is an observed interval (i.e. it is calculated from the observations), in principle different from sample to sample, that frequently includes the parameter of interest, if the experiment is repeated.
Steps for Confidence Interval:
- Determine the confidence level: This is the probability that the interval contains the true value of the parameter. Typically a 95% confidence level is used, which means that the true value of the parameter is contained within the interval 95% of the time.
- Calculate the sample mean (x-bar) and sample standard deviation (s).
- Calculate the margin of error (ME): ME = t* (s/√n)
- Calculate the confidence interval (CI): CI = x-bar ± ME
- Interpret the results: The confidence interval provides an interval estimate of the true value of the population mean. The confidence level indicates the probability that the true value lies within the confidence interval.
Examples
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A confidence interval can be used to estimate a population parameter from sample data. For example, a 95% confidence interval for the population mean can be calculated from sample data to provide an interval within which the true population mean is likely to fall.
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A confidence interval can be used to compare two population means. For example, if the 95% confidence interval of one mean does not overlap with the 95% confidence interval of the other mean, it can be concluded that the two means are significantly different.
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A confidence interval can be used to measure the accuracy of a statistical model. For example, a 95% confidence interval for the accuracy of a regression model can be calculated to provide an interval within which the model’s accuracy is likely to fall.