# null and alternative hypotheses

A group of 50 complete a national fitness test and get a mean score of 80 out of 100. The national average is 72 with standard deviation 6. Can we conclude the group of 50 is fitter than the national average. Let ${\mu}$ be the national average score. What are the null and alternative hypothesis?

I'm really confused on this on. Its almost as if I should be using a difference of means test.

• The question does not ask you to conduct a test or even to propose one. All you need to do is state two hypotheses in terms of the information given.
– whuber
Nov 14, 2014 at 17:39

The null should be easy as it is almost always the same form, $H_0 = \mu =\mu_0$. However, the alternative can be one of the three:

$H_a: \mu \neq \mu_0$

$H_a: \mu > \mu_0$

$H_a: \mu < \mu_0$

To know what form of the alternative to use we must look at the research question. Here the research question asks "Can we conclude the group of 50 is fitter than the national average. Let μ be the national average score." which does indicate a direction. This is a single mean test as we have the true average national, so for the null we would have:

$H_0: \mu = 72$

The question is, does this group of 50 have a higher average than the national average? In other words, is the true average score of the group of 50 higher than the national average?