Lecture 10. TWO POPULATIONS TESTING Lecture 10. TWO POPULATIONS TESTING

 Two independent population  T-test for Means  Z-test for Proportion

 [1] Chapter 10:

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10.2 (p.452); 10.4 (p.466)

10.1. Independent Populations 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

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 Consumption and Income of households

Dependent & Independent Sample Dependent & Independent Sample

 Dependent sample  Independent samples

Firm A

Firm B

Store      

76 79 77 80 75 89

90 82 85 90 80 79

Before 72 75 70 82 70 83

After 76 79 77 80 75 89

87

Good Advertising policy ?

88

On average, are A and B really different?

84

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10.2. T-test for Means 10.2. T-test for Means

 Two independent Populations  Two independent Samples

Variable

Sample size

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Sample mean Sample variance Population 1 ) ~(, ̅ Population 2 ) ~(,

T-test for Means T-test for Means

Statistical value Hypothesis Reject H0

>

: = : >

̅ −

=

, > 30

< − + : = : <

> /

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: = : ≠

Example 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.

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(b) Estimate − of the test

10.3. Z-test for Proportions 10.3. Z-test for Proportions

Statistical value Hypothesis Reject H0

>

: ≤ : > =

+ ̅(1 − ̅)

̅ − ̅ 1 1

< −

: ≥ : <

̅ =

+ +

> /

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: = : ≠

Example 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 Own house 120 180 Rent house City B 150 150

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With significant level of 5%, testing the hypothesis that proportion of owned house in workers are not equal

Exercise Exercise

 Dependent Samples  Independent Samples  T-test for Means  Z-test for Proportion

Exercise Exercise

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[1] Chapter 10  (455) 9, 14, 15,  (468) 35, 36