Bài giảng Probability & Statistics - Lecture 10: Two populations testing - Bùi Dương Hải
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
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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)
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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
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Dependent & Independent Sample
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Dependent sample
Store Before After
72 76
75 79
70 77
82 80
70 75
83 89
Firm A Firm B
76 90
79 82
77 85
80 90
75 80
89 79
87
88
84
Independent samples
Good Advertising policy ?
On average, are A and B really different?
10.2. T-test for Means
Two independent Populations
Two independent Samples
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Population 1 Population 2
Variable ~ ( ,
) ~ ( ,
)
Sample size
Sample mean ̅
Sample variance
T-test for Means
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Statistical value Hypothesis Reject H0
=
̅ −
+
, > 30
: =
: >
>
: =
: <
< −
: =
: ≠
> /
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
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10.3. Z-test for Proportions
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Statistical value Hypothesis Reject H0
=
̅ − ̅
̅(1 − ̅)
1
+
1
̅ =
+
+
: ≤
: >
>
: ≥
: <
< −
: =
: ≠
> /
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
[1] Chapter 10
(455) 9, 14, 15,
(468) 35, 36
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Exercise
