Let X1,X2, . . . ,Xn be a random sample of size n from a normal population with mean µ and variance σ2. (a) Assuming that σ2 is known, find the equi-tailed 100(1 − α)% two-sided confidence interval for µ by inverting a test statistic. (b) Assuming that σ2 is unknown, find a pivotal quantity based on this random sample. Using the pivotal quantity, find the equi-tailed 100(1 − α)% two-sided confidence interval for µ.

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