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Suppose that X is a sample and a statistic T(X) has a distribution in a location family {P_µ: µ ∈ R}. Using T (X), derive a confidence interval for µ with level of significance 1 - α and obtain the expected interval length. Show that if the c.d.f. of T(X) is continuous, then we can always find a confidence interval for µ with confidence coefficient 1 - α for any α ∈ (0, 1).

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