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\begin{align*} H_{0}\colon & \mu _2^\star - \mu _1^\star = \log (\gamma _0) \\ H_{1}\colon & \left\{ \begin{array}{ll} \mu _2^\star - \mu _1^\star \ne \log (\gamma _0), & \mbox{two-sided} \\ \mu _2^\star - \mu _1^\star > \log (\gamma _0), & \mbox{upper one-sided} \\ \mu _2^\star - \mu _1^\star < \log (\gamma _0), & \mbox{lower one-sided} \\ \end{array} \right. \\ \end{align*}
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