Exam 13: Inference About Comparing Two Populations, Part 2

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Headache Medicine: A researcher wants to see if/how men and women differ in their reaction to a headache medicine with respect to drowsiness. In testing the hypotheses Headache Medicine: A researcher wants to see if/how men and women differ in their reaction to a headache medicine with respect to drowsiness. In testing the hypotheses   vs.   , the following statistics were obtained: n<sub>1</sub> = 400, x<sub>1</sub> = 208, n<sub>2</sub> = 250, and x<sub>2</sub> = 115, where x<sub>1</sub> and x<sub>2</sub> represent the number of patients in the two samples (men vs. women) who reported to have drowsiness as a result of taking headache medicine. -Estimate with 90% confidence the difference between the two population proportions. vs. Headache Medicine: A researcher wants to see if/how men and women differ in their reaction to a headache medicine with respect to drowsiness. In testing the hypotheses   vs.   , the following statistics were obtained: n<sub>1</sub> = 400, x<sub>1</sub> = 208, n<sub>2</sub> = 250, and x<sub>2</sub> = 115, where x<sub>1</sub> and x<sub>2</sub> represent the number of patients in the two samples (men vs. women) who reported to have drowsiness as a result of taking headache medicine. -Estimate with 90% confidence the difference between the two population proportions. , the following statistics were obtained: n1 = 400, x1 = 208, n2 = 250, and x2 = 115, where x1 and x2 represent the number of patients in the two samples (men vs. women) who reported to have drowsiness as a result of taking headache medicine. -Estimate with 90% confidence the difference between the two population proportions.

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The variance of the difference in sample proportions equals the difference of their population variances.

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When the necessary conditions are met, a two-tail test is being conducted at α\alpha = 0.05 to test  When the necessary conditions are met, a two-tail test is being conducted at  \alpha  = 0.05 to test   . The two sample variances are   and   , and the sample sizes are n<sub>1</sub> = 25 and n<sub>2</sub> = 25. The calculated value of the test statistic will be F = 2. . The two sample variances are  When the necessary conditions are met, a two-tail test is being conducted at  \alpha  = 0.05 to test   . The two sample variances are   and   , and the sample sizes are n<sub>1</sub> = 25 and n<sub>2</sub> = 25. The calculated value of the test statistic will be F = 2. and  When the necessary conditions are met, a two-tail test is being conducted at  \alpha  = 0.05 to test   . The two sample variances are   and   , and the sample sizes are n<sub>1</sub> = 25 and n<sub>2</sub> = 25. The calculated value of the test statistic will be F = 2. , and the sample sizes are n1 = 25 and n2 = 25. The calculated value of the test statistic will be F = 2.

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The pooled proportion estimate is used when:

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