How to compare gender proportions in a population?

Question

I want to test if more women are graduating from high school than men, the last ten years. I want to use percentages, not raw data. (2007-2017 percentages of women who graduated from high schools versus men)
And I also want to test if proportionally more women than men are graduating from high school than university. I can not use median because more people graduate from high schools than universities. I can use percentages (2007-2017 percentages of women who graduated from high school versus university)
What tests are the right ones?

user3808268 · Answer

For testing if (percent of women graduating) > (percent of men graduating)

Consider total number of data points to be $N$.

$p_w$  = proportion of women graduating in Sample.

$p_m$  = 1- $p_w$ = proportion of men graduating in Sample.

$sigma_{sample}$ = Standard deviation of the sample data = $sqrt{p_w*p_m}$

$sigma_{pop}$ = Standard deviation of the population = $frac{sigma_{sample}}{sqrt{N}}$

The null Hypothesis $H_0$ : $p_{w} = p_m$

The null Hypothesis $H_A$ : $p_{w} > p_m$

$Z =  frac{p_w-p_m}{sigma_{pop}}$

If $abs(Z)$ value is greater than 2, then the percent of women is greater than men.

Similarly, test for high school and university. Create the new dataset where only women are present. So, repeat the above steps.

$N$ = Total number of women

$p_h$ = percent of women in high school

$p_u$ = percent of women in university

How to compare gender proportions in a population?

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