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Tài liệu Lecture 3 về kiểm định giả thuyết trong thống kê, cung cấp kiến thức cơ bản về các loại giả thuyết và quyết định thống kê.
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Lecture 3 Hypothesis Test Đinh Thị Thanh Bình, PhD Faculty of International Economics, FTU 1 Testing hypothesis in Statistics - Revise • We have hypothesis that the average GPA of the students = 7.5. To test this hypothesis: H0: µ = 7.5 H1: µ ≠ 7.5 In which • µ: • H0 : • H1 : the average GPA in the population null hypothesis alternative hypothesis 2 Statistical decision
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Lecture 3
Hypothesis Test
Đinh Thị Thanh Bình, PhD
Faculty of International Economics, FTU
1
Testing hypothesis in Statistics - Revise
• We have hypothesis that the average GPA of the
students = 7.5. To test this hypothesis:
H0: µ = 7.5
H1: µ ≠ 7.5
In which
• µ:
• H0 :
• H1 :
the average GPA in the population
null hypothesis
alternative hypothesis
2
Statistical decision
Reject H0
True state of the null hypothesis
Do not reject
H0
Correct
Type II error
Type I error
Correct
H0 False
H0 True
3
• α : significance level
Highest probability accepted to get mistake type I
P(mistake type I) = P(reject H0/H0 right) ≤ α
• If there is evidence to reject H0, we say: reject H0,
accept H1
4
Testing hypothesis about the regression parameter
• 3 kinds of hypothesis test
H 0 : j = *j
2-sided:
-
-
right-sided:
*
H
:
1 j
j
H 0 : j *j
*
H1 : j j
left-sided:
H 0 : j *j
*
H1 : j j
5
Sampling distributions of the OLS
estimators
Assumption 7: The population error u is independent of
the explanatory variables X and normally distributed:
𝑢~𝑁(0, 2 )
Theorem 4.1: Normal sampling distribution
𝑗 ~N(𝑗 , var
𝑗 )
6
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