can you explain why the last answer is the right one but not the first option???

I was wondering the same... Maybe because we are talking about FEWER or less than (<) so we are left with AT LEAST or greater than or equal to (>=). So if you chose answer #1, we would have less than and more than but the 'just as many' would be left untested...

I think when we are wording the question with TEST/CHECK, we decide the current status is against what we are testing, so for Obama, we would test/check the statement of fewer orders, which means [H0 the current statute is aginst], and the [H1 else (what we actually test). so, I see (Option#4) is the most suitable answer.

The null hypothesis always has the following signs:  =  OR   ≤   OR    ≥

The alternate hypothesis always has the following signs:  ≠   OR  >   OR    <

Example: The average commute time for an ABC employee to and from office is at least 35 minutes.
What will be the null and alternate hypotheses in this case if the average time is represented by μ?
H₀: μ ≥ 35 minutes and H₁: μ < 35 minutes

Well, I would like to correct to the others how to chooes the null and alternative based on the question  the null hypothesis always have equal sign (=) thus Obama administration issued fewer executive orders this will be alternative hypothesis because he does not say equal and the null hypothesis will be greater than or equal or at least as many executive orders as the bush administration . the claim here is belong to alternative hypothesis hopfully that help otheres.