A demographer wants to know what proportion of women in different countries dye their hair. They take a random sample of women from Korea and another random sample of women from China. In Korea, 47% dyed their hair. In China, 56% dyed their hair. (a) What hypotheses would the demographer use to test if women in China are more likely to dye their hair than women in Korea? H0: pChina=pKorea vs. Ha: pChina ≠ pKoreaH0: pChina - pKorea = 0 vs. Ha: pChina - pKorea > 0 H0: μChina-μKorea = 0 vs. Ha: μChina-μKorea ≠ 0H0: pChina-pKorea = 0.09 vs. Ha: pChina-pKorea ≠ 0.09H0: μChina = 0.56 vs. Ha: μKorea = 0.47 (b) Suppose their test yielded a p-value of 0.079. What does this mean in the context of the test? We are 7.9% confident that the results of our test are correct.If the women of two countries have the same rates of coloring their hair, the probability of getting a difference at least this large is 0.079. If we take another sample, the probability of getting the same p̂China and p̂Korea is about 0.079.The probability that the women of the two countries have the same rate of coloring their hair is 0.079.7.9% of the time, we would expect the difference to be contained within 47% and 56%.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section: Chapter Questions

Problem 14T: An unbalanced coin is weighted so that the probability of heads is 0.55. The coin is tossed ten...

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A demographer wants to know what proportion of women in different countries dye their hair. They take a random sample of women from Korea and another random sample of women from China. In Korea, 47% dyed their hair. In China, 56% dyed their hair.

(a) What hypotheses would the demographer use to test if women in China are more likely to dye their hair than women in Korea?

H₀: p_China=p_Korea vs. H_a: p_China ≠ p_KoreaH₀: p_China - p_Korea = 0 vs. H_a: p_China - p_Korea > 0 H₀: μ_China-μ_Korea = 0 vs. H_a: μ_China-μ_Korea ≠ 0H₀: p_China-p_Korea = 0.09 vs. H_a: p_China-p_Korea ≠ 0.09H₀: μ_China = 0.56 vs. H_a: μ_Korea = 0.47

(b) Suppose their test yielded a p-value of 0.079. What does this mean in the context of the test?

We are 7.9% confident that the results of our test are correct.If the women of two countries have the same rates of coloring their hair, the probability of getting a difference at least this large is 0.079. If we take another sample, the probability of getting the same p̂_China and p̂_Korea is about 0.079.The probability that the women of the two countries have the same rate of coloring their hair is 0.079.7.9% of the time, we would expect the difference to be contained within 47% and 56%.

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