I want to test if a sample mean of 25 comes from a population with a
mean of 35, with a sample sigma of 4.0 . How do I write the null and
alternative hypothesis?

Hello existential,
The null hypothesis in this case would be:

H0: ? = 35

where ? is the population mean. That is, you want to test whether the
population mean is 35, despite the fact that the sample mean is 25.

The alternative hypothesis depends on whether you want to perform a
one- or a two-tailed test. This depends on what you are interested in
checking. You could either be interested in knowing if the population
mean is different from 35 (either higher or lower than that value); or
you may only be interested in checking, for example, if the population
mean is lower than 35.

You can find a good explanation of this at the following link:

HyperStat -- One- and two-tailed tests
http://davidmlane.com/hyperstat/A65596.html

"A probability computed considering differences in both directions is
called a "two-tailed" probability. The name makes sense since both
tails of the sampling distribution are considered. There are
situations in which an experimenter is concerned only with differences
in one direction. [...] For instance, if a new drug treatment is
developed, the main issue is whether or not it is better than a
placebo. If the treatment is not better than a placebo, then it will
not be used. It does not really matter whether or not it is worse than
the placebo"

So, if you are performing a two-tailed test, the alternative hypothesis would be

Ha: µ ? 35

If you are performing a one-tailed test, the alternative hypothesis could be either

Ha: µ < 35
or
Ha: µ > 35

More information on the concept of null hypothesis can be found at

HyperStat -- Null Hypothesis
http://davidmlane.com/hyperstat/A29337.html


Google search terms
"null hypothesis"
://www.google.com.ar/search?hl=es&q=%22null+hypothesis%22&meta=


I hope this helps! If you have any questions regarding my answer,
please don't hesitate to request a clarification. Otherwise I await
your rating and final comments.

Best wishes!
elmarto

---

Request for Answer Clarification by existential12-ga on 09 Jul 2005 20:07 PDT

Many thanks for your very clear answer, it confirms what I thought.
I'd use a one sided t-test in this case , correct ? To show that the
sample mean is very unlikley to come from the population..

---

Clarification of Answer by elmarto-ga on 09 Jul 2005 20:43 PDT

Hi existential,
Thanks for the rating! Without any details about the nature of the
experiment, and given that the sample mean appears to be significantly
smaller than the assumed population mean, I would also use a
one-tailed test, so that the alternative hypothesis would be that the
pop. mean is smaller than 35.

Best regards,
elmarto