If we want to test proportions, one wrong way to do so is to put the proportions themselves directly into the chi-square formula, convert proportions to frequencies, or take the difference in proportions and turn it into a z score.
Added by Hector H.
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Converting proportions to frequencies: This is actually a correct way to test proportions, as long as you have the sample sizes for each group. You can multiply the proportions by the sample sizes to get the frequencies, and then use those frequencies in a Show more…
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Find the value of $z *$ that would be used to test the difference between the proportions, given the following:
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Extending the Concepts and Skills Chi-Square Homogeneity Test and Two-Proportions z-Test. As we mentioned on page $619,$ the chi-square homogeneity test for comparing two population proportions and the two-tailed two-proportions $z$ -test are equivalent; that is, they always yield the same result. In the following exercises, you are to establish that fact. Foreign Affairs. Refer to Excrcise 13.95 and show that the value of the $x^{2}$ -statistic cquals the square of the value of the z-statistic. (Note: You may observe slight differences due to roundoff error.
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Chi-Square Homogeneity Test
The chi-square test is more appropriate than the t-test for the comparison of two proportions. a. Why? b. What type of variables are used in chi-square analysis?
Sri K.
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