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![]() ![]() To construct a confidence interval estimate for an unknown population mean, we need data from a random sample. When the population standard deviation σ is known, we use a normal distribution to calculate the error bound.X ¯ X ¯ is normally distributed, that is, X ¯ X ¯ ~ N ( μ X, σ n ) ( μ X, σ n ).In summary, as a result of the central limit theorem, the following statements apply: Mathematically, alpha can be computed as α = 1 − C L α = 1 − C L. ![]() 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 ) ( 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, ( x ¯ – E B M, x ¯ + E B M). The confidence interval ( CI) estimate will have the form The sample mean, x ¯, x ¯, is the point estimate of the unknown population mean, μ. Here, the margin of error 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 x ¯ x ¯ as an estimate for μ, and we need the margin of error. ![]()
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