【正文】 ating a large sample of normal data andthen analyzing it with both the z and tdistribution routines.Proportions and Binomial Experiments Pg 35 . April 01, Breakthrough Management Group. Unpublished proprietary work available only under license. All rights reserved. April 3, 2001 Proportion data is usually the result of a binomialtypeexperiment Binomial experiments (or Bernoulli trials) are those thathave only one of two outes, either a “success” or a“failure” The probability of this type of experiment is described by abinomial distribution, a plicated distribution In many cases the normal distribution can be used toapproximate the binomial distribution When nxp 5 and nx(1p)5 μ= nxp and σ 2 = nxpx(1p)Binomial distributions are discussed inalmost every statistics textbook. Calculationswith them is not necessarily difficult, but it istedious if it must be done manually. Minitabhas routines, however, that greatly simplifiesthe calculations.If the binomial approximation applies andthe data can be estimated with a normaldistribution other statistical tests and controlcharts can be used that would not be availableotherwise.Try to construct your experiments suchthat the binomial approximation is valid.A general rule of thumb: for the normalapproximation to apply, have a sample size ofat least 30 and large enough to guarantees atleast 5 successes. 假設(shè)測試:Introduction to Hypothesis TestingA Bright IdeaNotes:Pg 5 11 Nov 2000 ?April 01, Breakthrough Management Group. Unpublished proprietary work available only under license. All rights reserved. A light bulb pany is trying to produce a brighter light bulb for thesame energy. It is hoped that a change in the filament coatingprocess will produce a brighter light. The engineer collected the last ten light bulbs made before theprocess change and the first ten after the change. The mean lightoutput of the old process bulbs is 1251 lumens and the new processis 1273 lumens. Does the increase of 22 in the means of the two groups represent areal improvement? Could the difference between these two groups have happened byrandom chance? Should the engineer switch to the new process?These kinds of problems are veryfamiliar to engineers. An engineer isgiven a task to improve a process orproduct. After a change in the process,the engineer is left with the problem ofdetermining whether the process changehas made a significant improvement ornot. Though engineers often use moreadvanced techniques to determine theimproved settings (DOE, for example, tobe discussed later), a hypothesis test isoften used to verify the experimentresults.The process may be as follows:?Identify the problem.?Design and run an experiment tofind an improved condition.?Analyze the data and determine theimproved operating point.?Verify the effectiveness of theimprovement with a hypothesis test.A Few Illuminating Details QC data were available for light bulbs produced in the same factory.All of the bulbs had been produced using the standard filamentcoating process. The data was prised of the averages of 10samples from consecutive batches of light bulbs. The engineercalculated the differences between consecutive groups and recordedit in a Minitab worksheet in column QCData. Considering the new data, the question now bees:“How often has the mean brightness of a groupof light bulbs been 22 lumens brighter than thegroup produced immediately before?” Open Minitab worksheet for the dataIn the Minitab datasheet, column‘OldData’ is the first set of 10 from theold process.‘NewData’ is the set of data from the newprocess.‘PlantData’ is the 210 averages of 10consecutive measurements from the oldprocess in sample order.‘Diff’ is the magnitude of the differencebetween consecutive groups.What Is a Hypothesis Test? A hypothesis test is simply paring reality to anassumption and asking, “Are they the same?”O(jiān)r A hypothesis test is testing whether real data fits a modelOr A hypothesis test is paring a statistic to a hypothesis 均值測試:Means Tests1. State the practicalproblem2. State the null hypothesis3. State the alternatehypothesis4. Test the assumptions ofthe data*5. Calculate theappropriate test statistic(or calculate pvalue)6. Lookup the critical valuefrom the appropriatedistribution (or set alpha)7. If the calculated statisticmeets the decision rulecriteria (or if pvalue α )then reject H08. Formulate the statisticalconclusion into apractical solutionThis is the general recipe for hypothesistesting. The tests differ in the appropriatestatistics and appropriate distributions.The means tests recipe is the same as waswhat learned for variance testing.Example – One Mean Vs. Target Background – A pany audits its stock of tennis balls by testing the bounceheight of 10 randomly selected balls. The average bounce height of thesample is in. The historical data is μ= and σ = . Has storagedegraded the bounce of the tennis balls? Use α = .1. State the practical problem: Is the bounce height of the stored population less than the historicalvalue?2. State the null hypothesis H o : μstored = 3. State the alternate hypothesis H A : μstored 4. Test assumptions: normality of the data pvalue = – Data is normalA very mon test is sampling stockfrom the warehouse for conformity to astandard.This example has a tennis ball panychecking whether the balls in storage stillmeet the bounce specification.Exercise – Mean Vs. Target Some local farmers believe that this year’ssoybean crop has an exceptionally high yield. Thestatewide average yield for the past five years has been520 bushels/acre with a standard deviation of 117.Thirtysix farms were sampled and the data is inworksheet Is this year’s soybean yield exceptional?Use α = .05.Ztest Exercise Solution1. State the practical probl