# One-Sample z-Test

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?

Michael M 05/16/2018.

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.