Consider a two-sided confidence interval for the mean when or is known: where

a, a, a.lfa,

a, a/2, we have the usual 100(-a)% confidence interval for u. In the above, when

a, a, the interval is not symmetric about The length of the interval is La(+)/V. Prove that the length of the interval is minimized when a = a = a/2. Hint: Remember that ) = 1-a so (-a), and the relationship between the derivative of a function y = f(x) and the inverse x=(y) is (d/dy)f(y) = 1/[(d/dx)f(x)]-