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When you conduct a 1 sample t-test why does minitab only give an upper bound or a lower bound for a confidence interval? So if $H_0: \mu = \mu_0$ and we test $H_a: \mu < \mu_0$ or $H_a: \mu > \mu_0$ why is only an upper bound or lower bound of a confidence interval returned respectively? Whereas testing $H_a: \mu \neq \mu_0$ returns both a lower and upper bound.

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Do you mean "or $H_a : \mu\geq\mu_0$"? – Scortchi Jan 10 '13 at 14:52
@Scortchi: yes i do – James Jones Jan 10 '13 at 14:54

It depends on the options you supply for the alternative hypothesis: "less than", "not equal", or "greater than" $\mu_0$. If you're doing a one-sided test, Minitab assumes you're interested in a one-sided confidence interval. And it makes sense to assume that if you're interested only in testing whether the population mean's higher than a certain value, you'd also be interested in saying that values of the mean lower than a certain bound are implausible.

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