# Alternative hypothesis when null hypothesis is ambiguous?

This is more of a textbook semantics issue. Is the alternative hypothesis always two-tailed when all that is known is a null hypothesis $H_0$ where $p$ equals some arbitrary figure, where an arbitrary sample proportion and significance level are also given (assuming all requirements are met)?

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When your H0 is "p=something" and your Ha is "p≠something", then yes, a two-tailed test is what's needed. "One tailed" replaces the "≠" with ">" or "<", whichever is appropriate. – non-expert Jan 4 '11 at 5:16

Yes, although it's more than just a textbook semantics issue. In the absence of information about the form the alternate hypothesis should take (e.g., in the absence of a research question like "Does the new drug work better than the best-known drug on the market?") then the formulation of the alternate should just be the negation of the null. Thus the form of $H_0$ and $H_a$ should be $p = p_0$ and $p \neq p_0$, respectively. As non-expert points out in the comments, this then means that you need to perform a two-tailed test.