lecture11 notes

# Probability and Statistics for Engineering and the Sciences (with CD-ROM and InfoTrac )

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Stat 312: Lecture 11 Hypothesis testing Moo K. Chung [email protected] Oct 20, 2004 Concepts 1. The null hypothesis H 0 is a claim about the value of a population parameter. The alternate hypothesis H 1 is a claim opposite to H 0 . 2. A test of hypothesis is a method for using sample data to decide whether to reject H 0 . H 0 will be assumed to be true until the sample evidence suggest otherwise. 3. A test statistic is a function of the sample data on which the decision is to be based. 4. A rejection region is the set of all values of a test statistic for which H 0 is rejected. 5. Type I error : you reject H 0 when H 0 is true. P (Type I error) = P (reject H 0 | H 0 true) = α. The re- sulting α is called the significance level of the test and the corresponding test is called a level α test . We will use test procedures that give α less than a specified level (0.05 or 0.01). Class example I believe that dogs are as smart as people. As- sume IQ of a dog follows X i N ( μ, 10 2 ). IQ of 10 dogs are measured: 30, 25, 70, 110, 40, 80, 50, 60, 100, 60. We want to test if dogs are as smart as people by testing H 0 : μ = 100 vs. H 1 : μ < 100 . One reasonable thing one may try is to see how high the sample mean is. > x<-c(30, 25, 70, 110, 40, 80, 50, 60,
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