The confidence interval was previously defined as:
$$\hat{p} \pm z^* \text{s.e.}(\hat{p})$$
This standard error function,
$$\text{s.e.}(\hat{p}) = \sqrt{\frac{p(1-p)}{n}}$$
is highest when \(\hat{p} = 0.5\). This transforms the expression into:
$$\hat{p} \pm \frac{z^*}{2\sqrt{n}}$$
This is called the conservative confidence interval, since it is the largest that a confidence interval can be given a sample size.
This can help you choose a sample size, given a conservative margin of error that you want.
$$m = \frac{z^*}{2\sqrt{n}}$$
This can be rearranged to:
$$n = \left(\frac{z^*}{2m}\right)^2$$
Make sure to always round up, because you can't have 0.2 of a sampled element. This is the minimum, so round up.
The null hypothesis \(H_0\) is the hypothesis that says there is no effect. This is a statement about the population parameter, not the sample statistic.
The alternative hypothesis \(H_a\) is the hypothesis that something is happening.
As a side note, the equals sign is always in the null hypothesis.
If you are looking at significant change in a direction, it is called a one-tailed hypothesis test. If you are looking at significant change from some value in either direction, then you should use a two-tailed hypothesis test.