Lecture 10-tests of hypotheses I

# Lecture 10-tests of hypotheses I - 1036: Probability &amp;...

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Prob. & Stat. Lecture10 - one-/two-sample tests of hypotheses (cwliu@twins.ee.nctu.edu.tw) 10-1 1036: Probability & Statistics 1036: Probability & 1036: Probability & Statistics Statistics Lecture 10 Lecture 10 One One - - and Two and Two - - Sample Sample Tests of Hypotheses Tests of Hypotheses

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Prob. & Stat. Lecture10 - one-/two-sample tests of hypotheses (cwliu@twins.ee.nctu.edu.tw) 10-2 Statistical Hypotheses • Decision based on experimental evidence whether – Coffee drinking increases the risk of cancer in humans. – A person’s blood type or eye color are independent variables. • A statistical hypothesis is an assertion or conjecture concerning one or more populations. – True of False is never known with absolute certainty unless the entire population is examined. – The decision procedure is done with the awareness of the probability of a wrong conclusion
Prob. & Stat. Lecture10 - one-/two-sample tests of hypotheses (cwliu@twins.ee.nctu.edu.tw) 10-3 Role of Probability in Hypothesis Testing • The acceptance of a hypothesis merely implies that the data do not give sufficient evidence to refute it. • Rejection means that there is a small probability of obtaining the sample information observed when the hypothesis is true . • Example: for the conjecture of the fraction defective p = 0.10, a sample of 100 revealing 20 defective items is certainly evidence of rejection – Since the probability of obtaining 20 defectives is approximately 0.002 The firm conclusion is established by the data analyst when a hypothesis is rejected

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Prob. & Stat. Lecture10 - one-/two-sample tests of hypotheses (cwliu@twins.ee.nctu.edu.tw) 10-4 Supporting a Contention • To reject the hypothesis • Contention: coffee drinking increases the risk of cancer Hypothesis: there is no increase in cancer risk produced by drinking coffee • Contention: one kind of gauge is more accurate than another Hypothesis: there is no difference in the accuracy of the two kinds of gauges
Prob. & Stat. Lecture10 - one-/two-sample tests of hypotheses (cwliu@twins.ee.nctu.edu.tw) 10-5 Null and Alternative Hypotheses • Structure of hypothesis – Null hypothesis, H 0 • any hypothesis we wish to test – Alternative hypothesis, H 1 • the opposite hypothesis to reject H 0 •E x a m p l e – H 0 is the null hypothesis p = 0.5 for a binomial population, – H 1 would be one of the following: p> 0.5, p< 0.5, or p 0.5

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Prob. & Stat. Lecture10 - one-/two-sample tests of hypotheses (cwliu@twins.ee.nctu.edu.tw) 10-6 Testing a Statistical Hypothesis • Rejection of the null hypothesis when it is true is called a type I error (level of significance). • Acceptance of the null hypothesis when it is false is called a type II error . • The probability of committing a type I error is denoted by α • The probability of committing a type II error is denoted by β
Prob. & Stat. Lecture10 - one-/two-sample tests of hypotheses (cwliu@twins.ee.nctu.edu.tw) 10-7 Example: α and β 0051 . 0 ) 7 . 0 , 20 ; ( ) 7 . 0 when 8 ( ) error II type ( 2517 . 0 ) , 20 ; ( ) when 8 ( ) error II type ( 0409 . 0 9591 . 0 1 ) , 20 ; ( 1 ) , 20 ; ( ) when 8 ( ) error I

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## Lecture 10-tests of hypotheses I - 1036: Probability &amp;...

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