A confidence interval is unbiased if the expected value of the interval midpoint is
Chapter 8, Problem 8.135(choose chapter or problem)
A confidence interval is unbiased if the expected value of the interval midpoint is equal to the estimated parameter. The expected value of the midpoint of the large-sample confidence interval (Section 8.6) is equal to the estimated parameter, and the same is true for the smallsample confidence intervals for and (1 2) (Section 8.8). For example, the midpoint of the interval y ts/ n is y, and E(Y ) = . Now consider the confidence interval for 2. Show that the expected value of the midpoint of this confidence interval is not equal to 2.
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