【正文】 f negative sideeffects is lower than %.The other branch of statistics isdescriptive. Its purpose is merely todescribe a set of measurements.Inferential statistics is used to guess whatGod knows about a population from a sample.Within inferential statistics, there are twotypes: estimation and hypothesis testing.Estimation is trying to guess the populationstatistics from a sample. Hypothesis testingconcerns evaluating a sample statistic andparing it to some hypothetical value.Estimates and the CLT
What is the best estimate of the population mean using sample data? The sample mean!
How good of an estimate is the sample mean? What factors influence the accuracy of the estimate of the meanfrom sample data? Recall that:
The variation in the distribution of sample means is a function of thevariance of the Population and the sample size!n Pop X /σ σ =What About Small Samples?
If the population standard deviation is known (it almost never is) usethe previous formula for small samples, too
If the population sigma is unknown (it usually is): The estimate for standard deviation (s) is used The tdistribution is used instead of the normal (Z) distribution
Q: What is a tdistribution? The tdistribution is a family of bellshaped (normallike)distributions that are dependent on sample size The smaller the sample size n, the wider and flatter thedistributionns t X μ ns t X n n 1 , 2 / 1 , 2 / +≤≤α αThe tdistribution is the general case forany sample where the population standarddeviation is unknown. However, with largesamples, the t and zdistributions are nearlyidentical, so either can be used.You can verify this in Minitab bygenerating 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 Unpublished proprietary work available only under license.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(cè)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(cè)試:Means Tests1. State the practicalproble