# Lecture 13 - Classes on Friday March 7 and Tuesday March 18...

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Classes on Friday, March 7 and Tuesday, March 18 are in the West Hall Auditorium

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The 5-Step Hypothesis Testing Procedure Step 1: Formulate the null and alternative hypotheses. Step 2: Pick the value of α and find the rejection region. Step 3: Calculate the appropriate test statistic. Step 4: Reject or fail to reject the null hypothesis. Step 5: Interpret the statistical decision in terms of the problem
Problem 8-19 (page 304) Small samples, type II error calculation

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8-19 95 : . 95 : .) 2 . 1 32 . 94 16 = = = = μ σ a o H vs H a x n 3 . 0 16 2 . 1 58 . 2 01 . 0 2 = = = = n Z α n Z Z 2 Reject to Fail 27 . 2 3 . 0 95 32 . 94 ± = =
b) () ( ) 2266 . 0 91 . 5 75 . 0 3 . 0 1 58 . 2 3 . 0 1 58 . 2 ' 2 ' 2 ' Φ Φ = Φ Φ = + Φ + Φ = n Z n Z o o σ μμ μβ α

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() 2266 . 0 9 . 5 75 . 0 77 . 95 23 . 94 9 . 5 3 . 0 94 77 . 95 75 . 0 3 . 0 94 23 . 94 3 . 0 , 94 ~ = = = = = Z P x P n N x β σ
c.) () ( ) 2 2 2 ? to obtain 0.01 94 0.10 95 94 1.2 2.58 1.28 95 94 21.46 22 n nZ Z n αβ α β σ = = = =+ =⇒ =

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Problem 8-30 (page 305) Large sample test procedure Problem 8-31 (page 306) Small sample test procedure Problem 8-35 (page 310) Large sample test on a proportion
8-30 115 11.3 6.43 nx s == = Want to "prove" 15 0.05 . : oa Hv s H μ α < = ≥< 6.43 0.6 115 s n Reject 17 . 6 6 . 0 15 3 . 11 65 . 1 = = = Z Z

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8-31 9 6.32 1.65 70 . 1 :7 . o oa nx s Hv s H μα μμ == = ≥< 9 65 . 1 397 . 1 8 , 1 . 0 8 , = = = n t t σ α

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• Spring '08
• MALMBORG
• Null hypothesis, Statistical hypothesis testing, large sample test, sample test procedure, test procedure Problem, 0.042 4.2%

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Lecture 13 - Classes on Friday March 7 and Tuesday March 18...

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