given a simple random sample of men and a simple random sample of women, we want
ID: 2957920 • Letter: G
Question
given a simple random sample of men and a simple random sample of women, we want to use a 0.05 sifnificance level to test the claim that the percentage of men who smoke is equal to the percentage of women who smoke. One approach is to use the P-value mehod of hypothesis tesing, a second approach is to use the tradtional method of hypothesis testing, and a third approach is to base the conclusion on the 95% confidence interval estimate of p1-p2. Will all three approaches always result in the same conclusion? Explain.
Explanation / Answer
Ok, in fact, all three are the same! First, hypothesis testing means we specify a null hypothesis, then we calculate the p-value, which is the probability that we observe values more extreme, given the null hypothesis is true! This is exactly the same as fixing a type I error probability, and then work backwards to see the rejection region! Again, confidence interval is exactly the acceptance region! So if the value observe in not within the CI, null hypothesis is now rejected. This is a little bit difficult to get when you are new to the idea, but once it sinks in, you will find it obvious. All the best! =)
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