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# Lec20A - Slide 16 Lec20 IOE/Stat 265 Fall 2009 IOE/Stat 265...

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IOE/Stat 265 Fall 2009 IOE/Stat 265, Fall 2009 Lecture #20A: Addendum 8-3 Test Population Proportion 8-X Test Normal Variance (or Std Dev) 8-X 8.5 Summary of Single Population Tests 1 Textbook Example 8.13 Small Sample Binomial Hypothesis Test Slide 16, Lec20 n = 20 cans placed on accelerated life test n 20 cans placed on accelerated life test x = number that survive test Warrantee will be modified if fewer than 90% Warrantee will be modified if fewer than 90% of cans are expected to survive. H 0 : p 0.9 versus H 1 : p < 0.9 : p 0.9 versus H Use α = 0.05 equation to solve for “c” See Appx A1: B(c;20,0.9) 0.05 ± x 15 (i.e. c =16) Use β equation to estimate Type II Error e.g. if p = 0.8 β = P(x 16 | p = 0.8) = 1 – B(15; 20, 0.8) = 0.63 2 Bottle Filling Example (Revisited) S t t d filli f d t t i Suppose automated filling of detergent requires σ 2 0.01 oz 2 otherwise an unacceptable number of bottles will be underfilled number of bottles will be underfilled. You sample n=20 bottles at random and observe s 2 = 0.0153 oz 2 0.0153 oz Should the machine be adjusted (assume α = 0.05) ? 3 Step by Step Approach Step-by-Step Approach 1) Identify the parameter of interest Identify the parameter of interest.

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Lec20A - Slide 16 Lec20 IOE/Stat 265 Fall 2009 IOE/Stat 265...

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