Hypothesis--Testing(ppt文档).ppt
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1、Hypothesis Testing Use SPSS to do hypothesis testing the general issues of Hypothesis testing parameters testing of one normal populationparameters testing of two normal populationthe small probability principle in Hypothesis testingThe concept of hypothesis testingThe steps of Hypothesis testingtwo
2、 type errors of Hypothesis testingTwo-tailed testing and one-tailed testing The P-value of hypothesis testing(10%,5%,1%)A factory produce a kin of canned goods to export,Experience has shown that the net weight of canned subject to the normal distribution.Standard specifications is that the net weig
3、ht of each tank is 250 grams,the standard deviation is 3 grams.Now,on the line,we can carry out 100 randomly to check,obtaining the average net weight is 251 grams.Whether or not the canned subject to the net weight specifications?sample mean Subject to normal distribution for the mean of 250 and th
4、e standard deviation of 0.3 250250supposing population subject to normal distribution forthe mean of 250 and the standard deviation of 3.0250.6249.4sample mean Subject to normal distribution for the mean of 250 and the standard deviation of 0.32510.95450sample mean Subject to normal distribution for
5、 the mean of 250 and the standard deviation of 0.32.00-2.003.33 subject to the normal distribution,that is 0acceptance region rejection regionrejection region critical value critical value Z statistic significance level Hypothesis testing is a method of statistical inference,Which first we make assu
6、mptions to population parameters for concern and unknown,then select samples and make use of the information of samples provided,finaliy according to the principles of the small probability to judge the accuracy of assumptions.Raising the null and alternative hypothesisA factory produce a kin of can
7、ned goods to export,Experience has shown that the net weight of canned subject to the normal distribution.Standard specifications for is that the net weight of each tank is 250 grams,the standard deviation is 3 grams.Now,on the line,we can carry out 100 randomly to check,obtaining the average net we
8、ight is 251 grams.Whether or not the canned subject to the net weight specifications?Identifying test statistic Providing significant level Significant level corresponding to the probability of rejecting real error,usually take =0.05,or =0.01,or =0.0455Calculating the value of the test statistic Mak
9、ing statistical decision Reject the null hypothesis,these canned foods dont coincide the specification of net weight.Type I error:The mistake of rejecting the null hypothesis when it is actually true.Also it is called the mistake of rejecting true.In the hypothesis testing,According to a sample of a
10、ll samples to a sample we test the hypothesis.However,the sample was random,and this allows us to make the decision-making there is the possibility of mistakes.the null hypothesis to be truethe null hypothesis to be falseType II error:The mistake of failing the null hypothesis when it is actually fa
11、lse.Also it is called the mistake of accepting false.four possible decision-making of Hypothesis testingH0 is trueH0 is falseReject H0Type I error(the mistake of rejecting true.)Correct decision Accept H0Correct decision Type II error(the mistake of accepting false)The probability of error for rejec
12、ting true is /2+/2=The probability of correct decision-making is 1-(true)采伪错误的概率为。The probability of correct decision-making is 1-。(false)We hope that the two types of offenders,the better the smaller the probability of error.However,two types of errors are not independent of each other.Reduce,will
13、lead to the increase;reduce,will rise to the increase.At the same time to reduce the probability of committing two types of error,the only way to increase the sample size.In Hypothesis testing practice,all in the implementation of such a principle:the most concern as the null Hypothesis made in orde
14、r to be more serious consequences of the error on,prior to control.relation of and A company design an air bag,when a traffic accident occurred,the air bag can play a role in the protection of the buffer to the driver.The company that designed the air bag in the event of traffic accidents is not jus
15、t the moment more than 0.2 seconds to charge air and play a good cushion.Practice has proved that if its air time is more than 0.2 seconds,it will have no time to play a role in the protection of the buffer to the driver and one was injured.Try to raise the reasonable null hypothesis on the issue.Fo
16、rmulation 1Formulation 2(feasible)H0:0.2 SecondsH1:0.2 SecondsH0:0.2 SecondsH1:0.2 SecondsType I errorThe average inflation less than 0.2 seconds,but reject H0 and think that fail.This makes companies to lose business opportunities.The average inflation more than 0.2 seconds,but reject H0 and think
17、that is qualified.This makes person or body injuries and deaths.Type II errorThe average inflation more than 0.2 seconds,but think that it less than 0.2 seconds and accept H0.This maybe make person or body injuries and deaths.The average inflation not more than 0.2 seconds,but accept H0 and think th
18、at is qualified.This makes companies to lose business opportunities.Two-tailed testingone-tailed testingA factory processes a kind of part,accordding to experience know that ellipticity of parts asymptotic subject to normal distribution,the population mean for 0.081mm,the population standard deviati
19、on for 0.025mm.Another new machine use to process,taking 200 parts to test,and geting elliptical mean for 0.076mm.Asked it has any significant difference that the new machine process population mean of ellipticity of parts with the previous.acceptance regionrejection regionrejection regionTwo-tailed
20、 testingA wholesaler want to buy light bulbs from a number of manufacturers,according to the terms of the contract,the service life of light bulbs can not be lower than 1,000 hours.Known the service life of light bulbs to be subject to normal distribution,the standard deviation for 20 hours.In popul
21、ation randomly selected 100 light bulbs,have lent their mean for 960 hours,should the wholesalers buy these bulbs.acceptance regionrejection regionLeft testingCritical valueTelevision sets CRT quality standards of the production is an average service life for 1200 hours,the standard deviation of 300
22、 hours.A TV factory that its CRT production quality far surpass the required standards.In order to verify,randomly selected 100 samples,measured the average service life for 1245 hours.Can we say the quality of picture tubes is significantly higher than the required standards.acceptance regionreject
23、ion regionRight testingP-value,when the null is true,gets the probability of the observing data or extreme data values.acceptance regionrejection regionrejection regionTwo-tailed testing,if P value/2,rejectH0P-value can be used to compare with the significant level compared,to do testing and decisio
24、n-making,and provides the emergence probability of samples value of in a certain scope.acceptance regionrejection regionacceptance regionrejection regionOne-tailed testing,if P value,reject H0 mean test in variance known mean test in variance unknownhypothesis testing of population rateA factory pro
25、cesses a kind of part,accordding to experience know that ellipticity of parts asymptotic subject to normal distribution,the population mean for 0.081mm,the population standard deviation for 0.025mm.Another new machine use to process,taking 200 parts to test,and geting elliptical mean for 0.076mm.Ask
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