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Suppose we construct $95 \%$ confidence intervals for the population mean from $100$ random samples from a normally distributed population with mean $\mu$ and variance $\sigma^2$ of a data set. Is it common to construct hypothesis tests based on these confidence intervals? In other words, can we use confidence intervals to inform us as to what the best hypothesis test is to construct (i.e. the one with the highest power)?

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This sounds an awful lot like the recent question at stats.stackexchange.com/questions/48228. It is based on the same missing information: namely, an absence of any reference to an alternate hypothesis. Please clarify. – whuber♦ Jan 22 at 21:58

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