Consider K(>2) independent populations π1,..,π k such that observations obtained from π k are independent and normally distributed with unknown mean µ i and unknown variance θ i i = 1,…,k. In this paper, we provide lower percentage points of Hartley's extremal quotient statistic for testing an interval hypothesisH 0 θ [k] θ [k] > δ vs. H a : θ [k] θ  ≤ δ , where δ ≥ 1 is a predetermined constant and θ [k](θ ) is the max (min) of the θi,…,θ k . The least favorable configuration (LFC) for the test under H 0 is determined in order to obtain the lower percentage points. These percentage points can also be used to construct an upper confidence bound for θ[k]/θ.
Communications in Statistics: Simulation and Computation 26(2), pp.443-465