# slide7 - Inference on Mean, Var Unknown Replace with the...

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1 Inference on Mean, Var Unknown ± Replace σ with the sample variance, S. ± So if the test is: ± H 0 : µ = µ 0 ± H 1 : µ≠µ 0 ± The test statistic then becomes ± ± Use normal distribution if n is large. n / S X T 0 0 µ = 2 The t Distribution ± Again, the test is: ± H 0 : µ = µ 0 ± H 1 : 0 ± The test statistic is: ± ± Where T follows a t distribution with n – 1 degrees of freedom. n / S X T 0 0 =

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3 Rejection region for the t-test ± For a two-tailed test: ± Reject if |t| > t α /2,n–1 ± For an upper-tail test: ± Reject if t > t α ,n–1 ± For an lower-tail test: ± Reject if t < t α ,n–1 4 Example: Tensile Adhesion Test ± The mean load at failure is assumed to no more than 10 MPa. The sample mean, in a sample size of 22, was 13.71. And, the sample standard deviation was 3.55. Should we accept the null hypothesis at the α = 0.05 level?

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## This note was uploaded on 05/05/2008 for the course IE 121 taught by Professor Perevalov during the Spring '08 term at Lehigh University .

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slide7 - Inference on Mean, Var Unknown Replace with the...

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