Stat 312: Lecture 11 Hypothesis testing Moo K. Chung [email protected]Oct 20, 2004 Concepts 1. The null hypothesis H0 is a claim about the value of a population parameter. The alternate hypothesis H 1 is a claim opposite to H0 . 2. A test of hypothesis is a method for using sample data to decide whether to reject H0 . H0 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 H0 is rejected. 5. Type I error : you reject H0 when H0 is true. P (Type I error) = P (reject H0 | H0 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,
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