![]() If the confidence level (CL) is 95%, then we say that "We estimate with 95% confidence that the true value of the population mean is between 4.5 and 9.5." A confidence interval for a The confidence interval is (7 − 2.5, 7 + 2.5) calculating the values gives (4.5, 9.5). The sample mean is 7 and the error bound for the mean is We know the sample mean but we do not know the mean for the entire population. ![]() Suppose we have collected data from a sample. α is the probability that the interval does not contain the unknown population parameter. There is another probability called alpha (α). Higher because that person wants to be reasonably certain of his or her conclusions. Most often, it is the choice of the person constructing the confidence interval to choose a confidence level of 90% or However, it is more accurate to state that the confidence level is the percent of confidence intervals thatĬontain the true population parameter when repeated samples are taken. The confidence level is often considered the probability that theĬalculated confidence interval estimate will contain the true population parameter. The margin of error depends on the confidence level (abbreviated CL). ![]() (point estimate - error bound, point estimate + error bound) or, in symbols, The confidence interval estimate will have the form: The sample mean is the point estimate of the unknown population mean µ Here, the margin of error isĬalled the error bound for a population mean (abbreviated EBM). Download for free at 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. Available under Creative Commons-ShareAlike 4.0 International License.
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