09_ppt

# 09_ppt - Outline STAT 1302 Probability and Statistics II...

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Outline STAT 1302 Probability and Statistics II Example Class 9 Department of Statistics and Actuarial Science, University of Hong Kong [email protected] April 2008 Solution April 2008 1 / 13

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Outline Outline 1 Review Chapter 5. 2 Question 1 3 Question 2 Solution April 2008 2 / 13
Review Chapter 5. Question 1 Question 2 Hypothesis test Hypothesis test NB: Solution April 2008 3 / 13

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Review Chapter 5. Question 1 Question 2 Hypothesis test Hypothesis test I H 0 vs H 1 NB: Solution April 2008 3 / 13
Review Chapter 5. Question 1 Question 2 Hypothesis test Hypothesis test I H 0 vs H 1 I α (threshhold level, signiﬁcant level, size of the test) NB: Solution April 2008 3 / 13

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Review Chapter 5. Question 1 Question 2 Hypothesis test Hypothesis test I H 0 vs H 1 I α (threshhold level, signiﬁcant level, size of the test) NB: I α ↓ ⇒ harder to reject H 0 Solution April 2008 3 / 13
Review Chapter 5. Question 1 Question 2 Hypothesis test Hypothesis test I H 0 vs H 1 I α (threshhold level, signiﬁcant level, size of the test) I T(X) (T(x)) NB: I α ↓ ⇒ harder to reject H 0 Solution April 2008 3 / 13

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Review Chapter 5. Question 1 Question 2 Hypothesis test Hypothesis test I H 0 vs H 1 I α (threshhold level, signiﬁcant level, size of the test) I T(X) (T(x)) I p ( x ) ( = sup θ Θ 0 P ( T ( X ) > T ( x ) | θ ) ) NB: I α ↓ ⇒ harder to reject H 0 Solution April 2008 3 / 13
Review Chapter 5. Question 1 Question 2 Hypothesis test Hypothesis test I H 0 vs H 1 I α (threshhold level, signiﬁcant level, size of the test) I T(X) (T(x)) I p ( x ) ( = sup θ Θ 0 P ( T ( X ) > T ( x ) | θ ) ) I C – critical region ( = { x : p ( x ) < α } ) NB: I α ↓ ⇒ harder to reject H 0 Solution April 2008 3 / 13

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Review Chapter 5. Question 1 Question 2 Hypothesis test Hypothesis test I H 0 vs H 1 I α (threshhold level, signiﬁcant level, size of the test) I T(X) (T(x)) I p ( x ) ( = sup θ Θ 0 P ( T ( X ) > T ( x ) | θ ) ) I C – critical region ( = { x : p ( x ) < α } ) NB: I α ↓ ⇒ harder to reject H 0 I C = { x : p ( x ) < α } = { x : T ( x ) > k } , where k is critical value. Thus, reject H 0 if p -value < α reject H 0 if T ( x ) > k . Solution April 2008 3 / 13
Review Chapter 5. Question 1 Question 2 Size and power 1 Power function ω ( θ ) = P ( X ∈ C| θ ) . Solution April 2008 4 / 13

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Review Chapter 5. Question 1 Question 2 Size and power 1 Power function ω ( θ ) = P ( X ∈ C| θ ) . I α = sup θ Θ 0 ω ( θ ) Solution April 2008 4 / 13
Review Chapter 5. Question 1 Question 2 Size and power 1 Power function ω ( θ ) = P ( X ∈ C| θ ) . I α = sup θ Θ 0 ω ( θ ) 2 Two types of error NB: Solution April 2008 4 / 13

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Review Chapter 5. Question 1 Question 2 Size and power 1 Power function ω ( θ ) = P ( X ∈ C| θ ) . I α = sup θ Θ 0 ω ( θ ) 2 Two types of error I Type I error: reject H 0 when it is true. NB: Solution April 2008 4 / 13
Review Chapter 5. Question 1 Question 2 Size and power 1 Power function ω ( θ ) = P ( X ∈ C| θ ) . I α = sup θ Θ 0 ω ( θ ) 2 Two types of error I Type I error: reject H 0 when it is true. I Type II error:accept H 0 when it is false.

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09_ppt - Outline STAT 1302 Probability and Statistics II...

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