Admissibility of the usual confidence interval for the normal mean

Suppose that X1,…,XnX1,…,Xn are independent and identically N(μ,σ2)N(μ,σ2) distributed, where μμ and σσ are unknown parameters (μ∈Rμ∈R and σ>0σ>0). We prove that the usual confidence interval for μμ is admissible within a broad class of confidence intervals.