# The wording for null hypothesis

I'm new to this area and I'm a little confused with the wordings (although I've done a few calculations including T-Score tests...)

I just need to understand if the wording being used is correct.

Consider this: There are only a few lecturers who actually deliver practical knowledge to their students.

My question: Is it correct to state that the following are null hypotheses?

1. There are not many lecturers who deliver practical knowledge to their students.
2. The are only a few lecturers who deliver practical knowledge to their students.

To me, both convey the same meaning. But someone told me that the second statement is incorrect and that I must always include 'not' when forming a statement for null hypotheses.

• These seem like extremely poorly defined statements (what is "not many" or "a few")? Whether some more precise version of these make sense as null hypotheses depends on what question you wish to investigate. I do not think there is a need to state null hypotheses as a negation - in fact very often they are stated in a totally different manner (e.g. null hypothesis: parameter $\mu=0$, alternative hypothesis $\mu\neq 0$). Perhaps you misunderstood the statement or are not fully conveying the context, in which it was made? – Björn Sep 25 '16 at 14:15
• @Björn I just made up the case. Let's say, we want to show that graduates lack practical sills and we need to test if this is true. So based on that, do my statements 1 and 2 above make sense for a null hypothesis? BTW, you're correct about me not being too clear about the subject. I would really like to understand if we are allowed to phrase a null hypothesis like I have done above. Thanks! – itsols Sep 25 '16 at 14:38
• For a start, a null hypothesis needs to be clear. An imprecise statement like the above seems ill-suited for any question. If your re-phrasing, you just swapped "lecturers deleviring practical knowledge" to "graduates lacking practical skills", which does not really make this any clearer. In any case, I think you can phrase a null hypothesis with and without a negation, just not as imprecisely (as well as in a way that seems unsuitable for any kind of measurement) as you have done. – Björn Sep 25 '16 at 14:43
• The answers to this question might help you to clarify the meaning of null hypothesis. – T.E.G. Sep 25 '16 at 14:45
• Null hypotheses are precise statements about some characteristic of one or more populations (precise enough for it to be at least notionally possible to compute the distribution of the test statistic under the null). They are not vague statements and are not about samples. – Glen_b Sep 26 '16 at 0:44