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

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Stat 312: Lecture 11Testing on Population MeansMoo K. Chung[email protected]February 25, 2003Concepts1.P(Type I error) =P(rejectH0|H0true) =α.The resultingαis called thesignificance levelof the test and the corresponding test is calledalevelαtest. We will use test procedures thatgiveαless than a specified level (0.05 or 0.01usually).2. Testing meanμwith known varianceσ2.H0:μ=μ0vs.H1:μ < μ0Test statistic:z=¯x-μ0σ/n.Rejection region forlevelαtest:z≤ -zα.3. Testing meanμwith unknown varianceσ2.H0:μ=μ0vs.H1:μ < μ0Test statistic:t=¯x-μ0s/n.Rejection region forlevelαtest:z≤ -tα,n-1.4. Testing meanμwhen the sample size is large.H0:μ=μ0vs.H1:μ < μ0Test statistic:z=¯x-μ0s/n.Rejection region forlevelαtest:z≤ -zα.In-class problemsAssume the IQ of a dog followsXiN(μ,102).The IQ of 10 dogs are measured: 30, 25, 70, 110,40, 80, 50, 60, 100, 60. We want to test if dogs areas smart as people by testingH0:μ= 100 vs.H1:μ <100at levelα= 0