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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?

AdamO
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Vlad Gheorghe
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1 Answers1

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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.

Michael M
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  • Yes but in this exercise I had to decide what is H0 and H1 and I'm not even sure about that. – Vlad Gheorghe May 16 '18 at 19:55
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    Vlad, that is determined by a quick consideration of what would constitute evidence in favor of the assertion "dropped to 20%." For instance, if the true proportion were 21%, would this assertion be correct? What if the true proportion were 19%? – whuber May 16 '18 at 19:58