A student of the author surveyed her friends and found that among 20 males, 4 smoke and among 30 female friends, 6 smoke. Give two reasons why these results should not be used for a hypothesis test of the claim that the proportions of male smokers and female smokers are equal.
Given a simple random sample of men and a simple random sample of women, we want to use a 0.05 significance 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 method of hypothesis testing; a second approach is to use the traditional method of hypothesis testing; and a third approach is to base the conclusion on the 95% confidence interval estimate of p1â?"p2. Will all three approaches always result in the same conclusion? Explain.
Here is my explanation:
The first reason is the sample is not randomly chosen. In this case, it is limited to the friends. The second reason is for each of the two samples, the number of successes is at least 5 and the number of failures is at least 5. For male, p=4/20=0.25, np=20*0.2=4<5. ...
The solution provides detailed explanation as to the similarities and differences between p value method, hypothesis test and confidence interval method.