Resolved: hypothesis test formulation
In the example where the claim was a data scientist makes more than 125,000. Why H0 is set to "a data scientist makes more than 125,000", whilist it is the researcher's opinion, shouldn't be the alternative hypothesis?
Because that's Paul's claim, not yours.
You are doubting Paul's claim, your claim will be that the data scientists earn less than 125,000.
So you will run a test to see if Paul's claim is right or Yours.
Since the claim your trying to get is less than, then the rejection region will be on the left (negative sign)
If the test statistical z is higher than the rejection region, then accept Paul's claim. If not, reject it