Thank you for including some preliminary computations. You have $\hat p = 587/755 = 0.7775.$ You want to test $H_0: p = .75,$
perhaps against the 2-sided alternative $H_a: p \ne .75.$
Two-sided test. The test statistic is $$Z = \frac{\hat p - .75}{\sqrt{(.75)(.25)/755}} = 1.744,$$
which should be approximately standard normal if $H_0$ is true.
You'd reject $H_0$ at the 5% level, if $|Z| > 1.96,$ which is not
true, so you don't reject.
The P-value is the probability of a more extreme result than that observed.
For a two-sided hypothesis, that means 'more extreme in either direction',
so the P-value is
$$P(|Z| > 1.744) = 1 - P(|Z| \le 1.774) = 1 - P(-1.744 \le Z \le 1.744).$$
Using software, I got about $0.08,$ but you should compute it using
normal tables or whatever software you're expected to use in your class.
Right-sided test. If you were supposed to test against the one-sided alternative $H_a: p > .75,$
then you'd reject if $Z > 1.645,$ which is true. So you would reject $H_0.$
(You know that the estimate $\hat p > .75$, the question is whether it is
significantly larger, or whether .7775 could have just have happened
to exceed .75 due to random sampling error.)
For the right-tailed test, the P-value is
$P(Z > 1.774),$ the probability of a more extreme value in the direction of
the alternative. That P-value is half as big as for the two-sided test.
Note: You say you are doing a two-sided test. Not knowing the context of the problem, I can't say for sure that is right. So I'll let you
think about that as required.
(Suppose the purpose of the poll were to asses
the chances of passage of Proposition A in an upcoming election, and it
takes 75% Yes votes for passage. Then I'd suppose you'd want a one-sided
test. If lore from previous years is that 75% of the population thinks
it's morally wrong to cheat on income tax, and the purpose of the poll
is to assess whether that opinion has changed recently (one way or the other), then I'd suppose
you want a two-sided alternative.)
Sketches. In problems like this, it is always a good idea to draw
sketches so you can visualize the areas that match various probabilities.
In the left panel below (two-sided alternative), the heavy black line is the
observed value of $Z,$ the dotted black line is just as far from 0 as the
heavy black line, and the P-value is the sum of the two areas beyond the
black lines. The rejection region is values of $Z$ between the two red bars
(at 'critical values'); the total area under the density curve and outside the two red bars is 5%.
In the right panel (right-sided alternative), the heavy black line is again
the observed value of $Z.$ The red line is at the critical value, and 5% of
the area under the density curve to the right of the red bar. The rejection
region is to the right of the red line, and the observed value of $Z$ is
in the rejection region. The P-value (smaller than 5%) is the area to the
right of the observed value of $Z$.
