# How to test this kind statistical hypothesis ?

#### pajacek

##### New Member
Hey. How can I test $$H_{0} \: : \;\;\; \frac{\mu_{1} + \mu_{3}}{2}=\mu_{2}$$?

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#### BGM

##### TS Contributor
Usually exact test are rare. Even though in general you may form the likelihood ratio test statistic, the exact distribution is intractable and the critical region relies on simulation/numerical method. More common approach is forming the asymptotic tests.

But these are not the most important issues. The most important one is that: what is your data structure? model? assumptions?
Can you define your parameters more clearly? any likelihood function you can write down?

#### pajacek

##### New Member
I don't have specific data or assumptions. This is the problem submitted by one of professors as a matter of defending the thesis. But now I see that "+" is not shown properly and easy question has changed to huge one ...

$${H_{0} \: : \;\;\;\; \frac{{\mu_{1}} + {\mu_{3}}}{2}=\mu_{2}}$$

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