![]() ![]() α is the probability that the interval does not contain the unknown population parameter. α is related to the confidence level, CL. There is another probability called alpha ( α). Most often, it is the choice of the person constructing the confidence interval to choose a confidence level of 90% or higher because that person wants to be reasonably certain of his or her conclusions. However, it is more accurate to state that the confidence level is the percent 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 (abbreviated CL). (point estimate - error bound, point estimate + error bound) or, in symbols,( x ¯ – E B M, x ¯ + E B M x ¯ – E B M, x ¯ + E B M) The confidence interval 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 ( EBM) is called the error bound for a population mean (abbreviated 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. Suppose that our sample has a mean of x ¯ = 10 x ¯ = 10 and we have constructed the 90% confidence interval (5, 15) where EBM = 5. A confidence interval for a population mean, when the population standard deviation is known, is based on the conclusion of the Central Limit Theorem that the sampling distribution of the sample means follow an approximately normal distribution. ![]()
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