Alternate hypothesis with an Equal to sign

[nokia]

Dear Friends,

Suppose I am a stock analyst and I wish to prove that the ABC co’s avg/mean stock returns are statistically equal to the returns of the stock index. Wouldn’t my alternate hypothesis be ABC’s return = Index return.

However I had an understanding that null hypothesis must contain the = sign and its the opposite of what I am trying to prove. How to make sense with this rule here?

Thanks

[S2000magician]

For the purposes of the CFA exam, H₀ has the equal sign and H_a does not.

[nokia]

Thank you smagician.

So this means in reality we may have equal to sign with H_a as well if this is what i am trying to prove? Just for CFA we assume equal to sign only with H₀.

Please confirm.

[MakeYourselfGreatAga]

You may hav = on Ha so long as you reverse the acceptance/rejection interpretations.

[S2000magician]

@nokia

Thank you smagician.

So this means in reality we may have equal to sign with H_a as well if this is what i am trying to prove? Just for CFA we assume equal to sign only with H₀.

Please confirm.

That’s correct.

[tickersu]

@nokia

Thank you smagician.

So this means in reality we may have equal to sign with H_a as well if this is what i am trying to prove? Just for CFA we assume equal to sign only with H₀.

Please confirm.

Look into equivalence testing and noninferiority testing. It’s popular in medicine. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3019319/

Look at Table 1 for a quick overview, read the paper a bit if you’re interested in a general idea on how the methodology will be different.