Lecture Probability & statistics: Chapter 10 - Bùi Dương Hải

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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.

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Nội dung Text: 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 – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 6
10.3. Z-test for Proportions Statistical value Hypothesis Reject H0 : ≤ ̅ − ̅ > = : > 1 1 ̅ (1 − ̅ ) + : ≥ / : ≠ PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 7
Example Example 10.2. Random observe 100 male and 100 female visitors, then there are 25 males and 35 females buy good. With significant level of 5%, testing the statement that buying proportion in female is higher than that in male. Example 10.3. The data shows the number of workers stay in their own house or rent house in city A and B City A City B Own house 120 150 Rent house 180 150 With significant level of 5%, testing the hypothesis that proportion of owned house in workers are not equal PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 8
Exercise  Dependent Samples  Independent Samples  T-test for Means  Z-test for Proportion Exercise [1] Chapter 10  (455) 9, 14, 15,  (468) 35, 36 PROBABILITY & STATISTICS – Bui Duong Hai – NEU – www.mfe.edu.vn/buiduonghai 9