Let T be a statistic having the noncentral chi-square distribution χ2r(θ) (see §1.3.1), where θ > 0 is unknown and r is a known positive integer. Show that the c.d.f. FT,θ(t) of T is nonincreasing in θ for each fixed t and use this result to construct a confidence interval for θ with confidence coefficient 1 - α.