University:
California State University, Northridge
Course:
CE 101/L | Introduction to Civil Engineering and Lab
Academic year:

2003
Views:

268

Pages:

22
Author:

saminyxs

PROPORTIONS Distribution Relationships Binomial Normal Poisson Chi-Square Importance of values of n and p Confidence Interval Two Tails One Tail Hypotheses One proportion Two proportions Several proportions prop-2 Binomial Distribution utilized when two outcomes for each trial probability of success same for each trial there are n trials, where n is a constant the n trials are independent Many experiments can be cast into the model of a Binomial Experiment: For example, we can measure the heights of a sample of people, Define "success" as being 5'2" or less, and Now we can count the number of "successes" (i.e., ≤ 5'2") and the number of "failures" (i.e., > 5'2") Binomial Distribution is computationally cumbersome, and thus approximations are most frequently employed for the purpose of inference EXAMPLE Two different types of polishing solution are being evaluated for possible use in a tumble-polish operation for manufacturing interocular lenses used in the human eye following cataract surgery. Three hundred lenses were tumble-polished using the first polishing solution, and of this number 253 had no polishing- induced defects. Another 300 lenses were tumble-polished using the second polishing solution, and 196 lenses were satisfactory upon completion. At a = 0.01, is there reason to believe that the two polishing solutions differ? Η: Π, ΠΟ X=253p=0.8433 2300 Pa=0.6533 a=0.01; two-sided test C = 2.575 (from Formal distribution Jable) Jest Statistic:=npitnopa=253+196 = 0.7483 600 =(1-7)(+2) = {(0.7483)×0.2517) (90,000)}/2 = 0.0354 Z= (0.8433-0.6533)-0 0.0354 = 5.367 THUS since (2:5.367) > (c=2.575), we (strongly!) Reject Ho CHI-SQUARE ANALYSIS METHODS INVOLVING PROPORTIONS TEST OF HYPOTHESIS OF TWO OR MORE PROPORTIONS TEST OF VARIABLE INDEPENDENCE (BASED ON PROPORTIONS) GOODNESS OF FIT TEST (BASED ON PROPORTIONS) TEST OF HYPOTHESIS OF TWO OR MORE PROPORTIONS Given k sample sets, Ho: pi==... k = H₁: not all pi are equivalent; at least one pi is significantly different; the te sample sets were not all drawn from the same population at least one sample set was drawn from a different population 2 2/2 = ΣΣ (0-eij)2 i=1 j=1 eij with(k-1) dof prop-14 TEST OF HYPOTHESIS OF TWO OR MORE PROPORTIONS Samples of three kinds of materials, subjected to extreme temperature changes, pro- duced the results shown in the following table: Material A Material B Material C Total Crumbled 41 27 22 90 Remained intact 79 53 78 210 Total 120 80 100 300 Use the 0.05 level of significance to test whether, under the stated conditions, the probability of crumbling is the same for the three kinds of materials. SAMPLE SETS Material A 2 Material B 3 Material C Total 90 90 = 0.30 300 OUTCOMES Crumbled 41 1322 21136 812=24 (0,30*80) (0.30*120) (0.30%100) 13=30 Remained intact2=79 53 01227 Ca1=84 eaa = 56 (0.708120) (0.70x80) (0.70*100) 210 210 =0.70 300 178 233 = 70 Total 120 80 100 300 1.00

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