Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I've been given different answers to this question in different courses. Some professors say it is (using the example alternative hypothesis of $\mu > 3$):

$$H_0: \mu = 3$$ $$H_1: \mu > 3$$

Others say it is:

$$H_0: \mu \le 3$$ $$H_1: \mu > 3$$

How should I write my null hypothesis for 1-tailed tests?

share|improve this question

1 Answer 1

up vote 1 down vote accepted

In general, a hypothesis is a statement that a restriction is true, where a restriction takes the form $\theta\in \Theta_0$ with $\Theta_0$ is a strict subset of a parameter space $\Theta$. If the null hypothesis is defined as $$ H_0:\theta\in \Theta_0 $$ the alternative hypothesis is its complement $$ H_1:\theta\in \Theta_0^c. $$ By this formal definition, the second one is correct and the first one does not constitute a hypothesis test unless $\Theta=[3,+\infty)$, which is highly unlikely in application.

PS: The definition comes from Econometrics by Bruce E. Hansen, Chapter 8 .

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.