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Lecture Probability & statistics: Chapter 10 - Bùi Dương Hải

Lecture "Probability & statistics - Chapter 10: Two populations testing" has contents: Two independent population, T- test for Means, Z - test for Proportion. Invite you to consult the content. | Lecture Probability & statistics: Chapter 10 - Bùi Dương Hải Lecture 10. TWO POPULATIONS TESTING Two independent population T-test for Means Z-test for Proportion [1] Chapter 10: 10.2 (p.452); 10.4 (p.466) PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 1 10.1. Independent Populations Independent Populations: Female students vs Male students; Enterprises in Hanoi vs in HCMC Dependent Populations Macroeconomics score and Microeconomics score of student intake 59 Consumption and Income of households PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 2 Dependent & Independent Sample Dependent sample Independent samples Store Before After Firm A Firm B 72 76 76 90 75 79 79 82 70 77 77 85 82 80 80 90 70 75 75 80 83 89 89 79 Good Advertising policy ? 87 88 On average, are A and B really different? 84 PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 3 10.2. T-test for Means Two independent Populations Two independent Samples Population 1 Population 2 Variable ~ ( , ) ~ ( , ) Sample size Sample mean ̅ Sample variance PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 4 T-test for Means Statistical value Hypothesis Reject H0 : = > : > ̅− = : = + 30 : = > / : ≠ PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 5 Example Example 10.1. The survey of 100 customers, in which 40 are male and 60 are female, shows that: for the male, average consumption is $250, standard deviation is $11; for the female, average consumption is $256, standard deviation is 15. Assumed that consumption of both are normal distributed. (a) With significant level of 5%, test the hypothesis that on average, female consuming more than male. (b) Estimate − of the test PROBABILITY & STATISTICS