[See Steps] Show that, among all (1-α) 100 \% confidence intervals of the form x̄-z_k α • (σ)/(√n) \prec μ \prec x̄+z_(1-k)
Question: Show that, among all \((1-\alpha) 100 \%\) confidence intervals of the form \(\bar{x}-z_{k \alpha} \cdot \frac{\sigma}{\sqrt{n}} \prec \mu \prec \bar{x}+z_{(1-k) a} \cdot \frac{\sigma}{\sqrt{n}}\) the one with \(k=0.5\) is the shortest.
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