In superficie (o in isolamento dalla realtà) entrambe le affermazioni sembrano ugualmente inutili per l'obiettivo dello stato. Tuttavia, considerando il contesto, la seconda affermazione è chiaramente più utile.
Dichiarazione 2
w
w=px/(px+(1−p)z)
pxz
H0:x>z
Riscriviamo l'equazione per ottenere le condizioni necessarie per H0
(1−w)px=w(1−p)z
x=w(1−p)z/((1−w)p)
For
H0 to hold we have:
x=w(1−p)z/((1−w)p)>z
w(1−p)>(1−w)p
0.9(1−p)>0.1p
1−p>p/9
p<0.9
So, for your hypo that women were more likely to survive, all you need is to check that there were less than 90% women among the passengers. This is consistent with your assumption 2, which seems to imply that p≈1/2. Hence, I declare that statement 2 all but asserts that women were more likely to survive, i.e. it's quite useful for your goal.
Statement 1
The first statement is truly useless in isolation, but has a limited use in the context. If we pretend we know nothing about the event, then saying that x=0.9 tells us nothing about z, and whether x>z?
However, from that little that I know about the event - I haven't seen the movie - it seems unlikely that x≤z. Why?
We know from Assumption 2 that p≈1/2, so the total survival rate is
px+(1−p)z. If we assume that x≈z and p≈1/2 we get
px+(1−p)z≈x=0.9
In other words 90% of all passengers survived, which doesn't ring true to me. Would they make a movie and talk about it for 100 years if 90% of passengers survived? So, it must be that
x>>z and less than half of passengers made it.
Conclusion
I'd say that both statements support your hypo that women were more likely to survive than men, but Statement 1 does so rather weakly, while Statement 2 in combination with assumptions almost surely establishes your hypo as a fact.