this is a really simple problem but I'm still in doubt about the solution.
There's a population of workers and the goal is to see whether the rate of illegal workers has dropped to 20%. I have a sample of n=100 and the proportion of illegals is 30%. So this is what I've done:
$$H_0: p > 0.2$$
$$H_1: p <= 0.2$$
sd.error = 0.04
test statistic = (0.30 – 0.20) / 0.04 = 2.5
Now I'm in doubt about what to do. I know that p(z <= 2.5) = 0. 994, but I don't know which side of z to look at. What is my p value, 0.994 or 0.006?
There is a rule for lazy statisticians: If not even the sample supports $H_1$ (30% is not smaller than 20%), then it is hopeless to claim $H_1$ to hold for the whole population. So without checking your calculations, the p value is large, i.e. 0.994.