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# 655 Class Note for CS 54300 at Purdue

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COURSE
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TYPE
Class Notes
PAGES
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WORDS
KARMA
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This 8 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Purdue University taught by a professor in Fall. Since its upload, it has received 23 views.

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Date Created: 02/06/15
Probability Theory Vs Statistics In Probability Theory we define a model and ask how objects quotbehavequot in that model In Statistics we observe quotbehaviorquot of objects and ask what is the quotlikelyquot model that explains this behavior Estimating a parameter Let p be the probability that a person will vote for candidate A We are interested in quotestimatingquot 19 using a sample of n randomly selected persons Let 1571 be the number of persons voting for A among the n persons Observing 1571 what can we say about 19 Definition 1 A 1 q confidence interval for a parameterT is an interval t1t2 such that PI T E t1t2 Z 1 q In our experiment we take a confidence interval 29 25 6256 ifFPlt25 5orpgt56 q VOteS 55L 6715 Bounding q Let p gt 15 6 The expected number of votes in that case is hp 2 7205 6 We need to find 6 such that 1571 g np1 e E L 6 1 2921 256 The probability of that event is bounded by q S np 23 S e gwwxl g Testing Statistical Hypothesis A company applies for an FDA approval of a drug claiming that the drug performs better than known solutions or placebo Let p be the effective ratio of the new drug and p0 the effective ratio of previous treatments Two com peti ng hypothesis Horp povs H1rpgtpo The test n patients were treated with the new drug X7 1 ifF the treatment to patient 239 was successful else X7 O The decision procedure Accept H1 if gt C i1 else accept H0 Error Estimates Two types of errors 1 Type 1 error Accepting H1 when p g m The confidence level of the test or PrTypeIerr0r PrZ X7 gt 0 19 3 p0 7L1 2 Type II error Accepting H0 when p gt 190 The power of the test PrTypeIIerr0r PrZ Xi 3 Ch gt 190 71 Using ChernofF bound we can bound the probabilities of both events For a quotreasonablequot 04 ltlt 12 we need to take C gt 1 l enp0 Using this bound we get a lt e np0623 But in that case for p 6 290290 26 is close to 1 19 needs to be significantly far from p0 for acceptance with small 04 and

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