The hypothesis is that there is no difference in the proportion of all men and women in the city who intended to vote for Trump. The null hypothesis is that the proportion of men intending to vote for Trump is equal to the proportion of women intending to vote for Trump. The alternative hypothesis is that the proportions are not equal.
Let p represent the proportion of all men in the city who intended to vote for Trump, and q represent the proportion of all women in the city who intended to vote for Trump. The 10% rule states that the sample size is less than 10% of the population. The large counts rule states that np and nq are both greater than or equal to 10.
The z-score is calculated using the formula:
z = (p1 - p2) / √(p(1-p)(1/n1 + 1/n2))
After calculating the z-score, the conclusion can be made based on the critical value of z at the 0.05 significance level.