04_Testing_part1

04_Testing_part1 - Hypothesis testing What is hypothesis...

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NTHU MATH 2820, 2008, Lecture Notes Ch9, p.1 Hypothesis testing • What is hypothesis testing? Question 7.1 (What is a hypothesis testing question?) 1. observed data. x 1 ,...,x n 2. statistical modeling. Regard x 1 ,...,x n as a realization of random variables X 1 ,...,X n , and assign X 1 ,...,X n a joint distribution: ajo intcd f F ( ·| Θ ) , or a joint pdf f ( ·| Θ ) , or a joint pmf p ( ·| Θ ) , where Θ =( θ 1 ,..., θ k ) ,and θ 0 i s are f xed constants ,bu tthe i r values are unknown . 3. point estimation. What is the value of Θ ? Find a function of X 1 ,...,X n , Θ ,toest imate Θ or a function of Θ . 4. hypothesis testing. Separate into two sets 0 and A ,where 0 A = and 0 A = . Use the data X 1 ,...,X n to answer the question: which of the two hypotheses, H 0 : Θ 0 versus H A : Θ A is more favorable. made by Shao-Wei Cheng (NTHU, Taiwan) Ch9, p.2 Definition 7.1 (null and alternative hypotheses, simple and composite hypotheses, TBp.331,332,334) Question 7.3 (asymmetry between H 0 and H A ) Question 7.2 Is there a di f erence between the roles of H 0 and H A ? Can we arbitrary exchange the two hypotheses? Canweobta inanest ima teo f Θ and accept H 0 if ˆ Θ 0 and reject H 0 if ˆ Θ A ? Hint . Consider the case: X Binomial( n, p ) , H 0 : p =0 . 5v . s . H 1 : p 6 =0 . 5 , What if n =10 5 and ˆ p =0 . 50001? H 0 is called
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04_Testing_part1 - Hypothesis testing What is hypothesis...

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