Compare and Contrast French and American Political System

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Objectives of Lecture 10 After completing this lecture you should be able to: 1. conduct hypothesis testing for comparing two population means for large independent samples 2. conduct hypothesis testing for comparing two population means for small independent samples 3. conduct hypothesis testing for comparing two population means for small dependent samples 4. conduct hypothesis testing for comparing two population proportions for large independent samples drawn from binomial populations 5. understand the F-distribution and read critical values from F-tables 6. conduct hypothesis testing for comparing two population variances 7. conduct one sample Chi-Square tests 8. conduct Chi-Square tests for contingency tables 1 24 24.1 Two-Sample tests Comparing two population means: Independent samples Two independent samples are samples in which the reading in one sample is not related to or dependent upon the reading in the other sample. H0 Ha : : or or µ1 − µ2 µ1 − µ2 µ1 − µ2 µ1 − µ2 =δ ̸= δ δ 24.1.1 2 2 Case 1: n1 , n2 large, σ1 , σ2 known Use a Z− test with test statistic x 1 − x2 − δ ¯ ¯ Z= √ 2 ∼ N (0, 1) 2 σ1 σ2 + n2 n1 24.1.2 2 2 Case 2: n1 , n2 large, σ1 , σ2 unknown (1) Use a Z− test with test statistic x 1 − x2 − δ ¯ ¯ Z= √ 2 ∼ N (0, 1) σ1 ˆ σ2 ˆ + n2 n1 2 Example 1 A potential buyer of electric bulbs bought 100 bulbs each of two famous brands, A and B. Upon testing both these samples, he found that brand A had a mean life of 1500 hours with σ1 = 50 hours whereas ˆ brand B had an average life of 1530 hours with σ2 = 60 hours. Can it be concluded at 5% level of ˆ significance that the two brands differ significantly in quality? 24.1.3 2 2 Case 3: n1 , n2 small, σ1 , σ2 unknown but assumed equal, small independent samples from normal populations (2) Use a t− test with test statistic t= where s2 = p x1 − x 2 − δ ¯ ¯ √ ∼ tn1 +n2 −2 1

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