When an alternative hypothesis is $H _ { a } : \mu _ { 1 } - \mu _ { 2 } \neq 0$ the $P$-value is found by doubling the appropriate area under the $t$ curve.

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When the alternative hypothesis is $H _ { a } : \mu _ { 1 } - \mu _ { 2 } \neq 0$, we are testing for a two-tailed hypothesis. In this case, the $P$-value is found by doubling the area in the tail of the $t$ distribution that corresponds to the observed test statistic.

When an Alternative Hypothesis Is Ha:μ1−μ2≠0H _ { a } : \mu _ { 1 } - \mu _ { 2 } \neq 0Ha​:μ1​−μ2​=0

When an Alternative Hypothesis Is $H _ { a } : \mu _ { 1 } - \mu _ { 2 } \neq 0$