Hi
It is a good question !
Remember when you are performing a hypothesis testing, you are only checking if your data is giving you sufficient evidence (at a given significance level) whether you can accept or reject null hypothesis only. However it is important you identify the alternate space correctly. (Refer to a similar discussion within the ActEd notes in section 2.2 of Chapter 12).
Now, in case you change the alternate to mu < 100, you reference critical point is the 0.05 (and not the 0.95) point of the Normal distribution i.e. -1.6445 as you are now looking at the left of the mean space. So, in this example as your test statistic value is 1.768, you will end up accepting Ho (albeit incorrectly !).
Had you actually tested against mu <> 100, your reference critical points would be -/+ 1.96. As the observed test statistic value lies between these points, you actually can't reject the null hypothesis at 5% significance !!
Last edited: Mar 10, 2013