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%.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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%.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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