![]() These numbers can be verified by consulting the Standard Normal table. If we set Z α at 1.64 we are asking for the 90% confidence interval because we have set the probability at 0.90. ![]() If we chose Z α = 1.96 we are asking for the 95% confidence interval because we are setting the probability that the true mean lies within the range at 0.95. Z α is the number of standard deviations X ¯ X ¯ lies from the mean with a certain probability. The confidence level is defined as (1-α). α is the probability that the interval will not contain the true population mean. The analyst must decide the level of confidence they wish to impose on the confidence interval. This is where a choice must be made by the statistician. Notice that Z α has been substituted for Z 1 in this equation. This is the formula for a confidence interval for the mean of a population.
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