There seems to be some ambiguity or contradiction in how to correctly choose the null and alternative hypotheses, both online and in my instructor's notes. I'm trying to figure out if this stems merely from my lack of understanding or if there actually is a disagreement in the scientific community at large. I've seen the following two ideas on choosing $H_0$ and $H_a$
The null hypothesis is the status quo, the state of things already accepted and/or shown to be true by previous data. We assume it to be true and need convincing evidence to reject it. The alternative hypothesis is the one being proposed based on data from the experiment in question, and is assumed to be false unless the data supporting it can convincingly show otherwise.
The null hypothesis is always the one that includes the equality, and the alternative hypothesis is the complement to it. It doesn't matter whether the equality is the status quo or is being claimed by the researcher, it is always H0.
An example I made up myself for demonstrative purposes, I'm not looking for an actual solution. Only interested in the hypotheses:
A researcher believes that children in economically disadvantages areas are more likely to be raised in single-parent homes. He surveys 1000 children from such an area and finds that 317 of them are raised in a single-parent home. Can we conclude with 95% confidence that 30% or more of the children in economically disadvantages areas are raised in single-parent homes?
What would be the H0 and Ha in this case and why?
My professor provided the correct answer (for an equivalent question but with different numbers) to be
H0 : p >= 0.3; Ha : p < 0.3
With the rationale that H0 must include the equality, which in this case is greater or equal to 30%
. Her solution then failed to reject the null hypothesis
and concluded that the researcher's claim is therefore correct.
To me this seems like assuming the claim to be true to begin with and giving it the benefit of the doubt, which is the opposite of what I thought was the correct approach.
A professor in this related question Difference between "at least" and "more than" in hypothesis testing? seemingly took the same approach.
I wish I could talk to my professor about this, but unfortunately there's a significant language barrier.