Refer to Problem 2.23. For multinomial sampling, show how to obtain a confidence interval for AR by first finding one for log(1 – AR) (Fleiss 1981, p. 76).

Data from Prob. 2.23:

For two parameters, a confidence interval for θ₁ – θ₂, based on single-sample estimate θ̂_i, and interval (ʆ_i,u_i) for θ_i, i = 1, 2, is

Newcombe (1998b) proposed an interval for π₁ – π₂ using the score interval (ʆ_i, u_i) for π_i that performs much better than the Wald interval (3.4). It is (π̂₁ – π̂₂ – z_α/2 s_L, π̂₁ – π̂₂ + z_α/2 s_U), with

Show that it has the general form above of an interval for θ₁ – θ₂.