Timeline for Show the shortest confidence interval of a normal distribution

9 events

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Jan 26, 2017 at 20:29	history	edited	amoeba		edited tags
Dec 19, 2014 at 6:01	vote	accept	the_deuce
Dec 10, 2014 at 20:49	comment	added	whuber♦		It's still not quite right. When $\alpha\lt 1/2$ and $0\lt k \lt 1$, both $Z_{k\alpha}$ and $Z_{(1-k)\alpha}$ are negative and therefore the interval you have written is empty! The meaning of your question is evident only from the intended conclusion, which implies the optimal interval is given by $[\bar{X}+Z_{\alpha/2} \sigma/\sqrt{n}, \bar{X}+Z_{1-\alpha/2} \sigma/\sqrt{n}]$. (There are many other ways to write this interval, since $Z_\beta = -Z_{1-\beta}$ for all $0\lt \beta \lt 1$, but your expression is not among the correct ones.)
Dec 10, 2014 at 20:37	history	edited	the_deuce	CC BY-SA 3.0	edited body
Dec 10, 2014 at 18:38	answer	added	whuber♦		timeline score: 6
Dec 10, 2014 at 17:52	comment	added	whuber♦		You probably meant to write "...$Z_{(1-k)\alpha}$...". The signs in front of the $Z_{*}$ are also problematic.
Dec 10, 2014 at 7:51	history	edited	gung - Reinstate Monica	CC BY-SA 3.0	added tag; formatted
Dec 10, 2014 at 7:45	review	First posts
Dec 10, 2014 at 7:51
Dec 10, 2014 at 7:41	history	asked	the_deuce	CC BY-SA 3.0