When stating the null and the alternative hypothesis, is it always right to think that the alternative is “the one you actually want”, and the null “the one you want to reject”?
For example, let’s say you believe there are more than 100 TVs in a bulding: Ho <= 100; Ha>100. You want to reject there <= 100, and therefore accept >100.
I’ve always thought it like that, but I recently found many books and people that tell me is the opposite… (I do not care very much as long as I get the CFA questions right, but I’d rather understand it since I have time enough!)
Alternative hypothesis is the one which you believe, like in your example you belive that there are more than 100 tv so alternative hypothesis is greater than 100. Null hypothesis in simple terms we can say is the one which is conducted or is obtained from past data.
the question is not about rejecting null hypothesis or accepting alternative hypothesis, we run these test to see whcih one is correct and which one is not according to given samples.
so dont think in a way that we always wanted to reject alternative hypothesis
For the CFA exam, the null hypothesis is the one you want to reject in favor of the alternative hypothesis.
(Note that in statistician-speak, you never – _ never! _ – accept an hypothesis; you either reject it, or you fail to reject it.)
Note, therefore, that your choice of the null hypothesis will depend on your point of view. If someone from your firm claims that the annual return on their mutual fund is 8% (by which they mean at least 8%), then your null hypothesis is that r ≤ 8%, and the alternative hypothesis is that r > 8%. However, if a competitor claims that the annual return on their mutual fund is 8% (by which they mean at least 8%), then your null hypothesis is that r ≥ 8%, and the alternative hypothesis is that r < 8%.
Here is an illustration that works better for operations management, but it still greatly helped me to understand the situation:
A machine A produces widgets and in a batch of 100, you know that 10% is defective.
A saleperson claims that he can sell you another machine B and claims that only 5% of the production is defective, so p=5%. Now you think he is just b*llsh*tt*ng you, and you think that 10% is defective.
So one way of setting the hypothesis (the simplest one) is:
Ho: p=10%
HA:p<10%
why set it up like this? if you don’t reject the null, you don’t spend any money buying the machine B since it’s the same as the one you already have. If you reject it, you are going to commit to a hefty investment.
So basically, H0 is the status quo, and HA is the expensive alternative, so you want to make sure, with high confidence (95% or 99%) that you can reject the H0 and go for the improvement suggested by the alternative.