![]() ![]() The confidence interval is (7 – 2.5, 7 + 2.5), and calculating the values gives (4.5, 9.5). The sample mean is seven, and the error bound for the mean is 2.5.We know the sample mean, but we do not know the mean for the entire population. Suppose we have collected data from a sample.Mathematically, alpha can be computed as α=1−CL. Alpha is the probability that the confidence interval does not contain the unknown population parameter. Most often, the person constructing the confidence interval will choose a confidence level of 90 percent or higher, because that person wants to be reasonably certain of his or her conclusions.Īnother probability, which is called alpha ( α) is related to the confidence level, CL. However, it is more accurate to state that the confidence level is the percentage of confidence intervals that contain the true population parameter when repeated samples are taken. The confidence level is often considered the probability that the calculated confidence interval estimate will contain the true population parameter. The margin of error (EBM) depends on the confidence level (CL). (point estimate – error bound, point estimate + error bound) or, in symbols. The confidence interval (CI) estimate will have the form: The sample mean,, is the point estimate of the unknown population mean, μ. The margin of error for the population mean is called the error bound for a population mean (EBM). To construct a confidence interval for a single unknown population mean, μ, where the population standard deviation is known, we need as an estimate for μ, and we need the margin of error. Suppose that our sample has a mean of and we have constructed the 90 percent confidence interval (5, 15), where the margin of error = 5. A Single Population Mean Using the Normal DistributionĪ confidence interval for a population mean with a known standard deviation is based on the fact that the sample means follow an approximately normal distribution. ![]()
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