Hypothesis--Testing(ppt文档).ppt

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 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 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 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 the 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 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 assumptions 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 canned 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 weight 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 Making 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 all 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 false.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 rejecting 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 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 order 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 just 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.Formulation 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 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 that 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 deviation 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 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 population 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 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 regionrejection 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 decision-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 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 deviation 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 regionA 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 population randomly selected 100 light bulbs,have lent their mean for 960 hours,should the wholesalers buy these bulbs.solution 1:acceptance regionrejection regionA 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 population randomly selected 100 light bulbs,have lent their mean for 960 hours,should the wholesalers buy these bulbs.solution 2:acceptance regionrejection regionTelevision sets CRT quality standards of the production is an average service life for 1200 hours,the standard deviation of 300 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.solution 1:acceptance regionrejection regionTelevision sets CRT quality standards of the production is an average service life for 1200 hours,the standard deviation of 300 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.solution 2:acceptance regionrejection regionA machine create soap that the thickness of the standard is 5cm.Now we want to know whether the machine is good performance or not.We randomly select 10 soap sample,measure that an average thickness is 5.3cm and standard deviation is 0.3cm.Try to test the hypothesis of machinery in good working under 0.01 significance level.acceptance regionrejection regionrejection regionA car tire manufacturer claims that the average life of first level tire span more than 40000km under a certain vehicle weight and normal traffic conditions.We make random sample of 120 tire to test,measure that the mean is 41000km and standard deviation is 5000km.Known the tire life kilometers approximate normal distribution.On the basis these data can be made the conclusion that the manufacturers product and what he said are the same standard(=0.05).acceptance regionrejection regionpopulation variancetest statistics The distribution of test statistics under=0hypothesis rejection region known unknownA list to statistics and rejection region for mean test of a normal populationIn the past few months a golf course have 20%female.In order to increase the ratio of female sports,golf course attract female sports in special manner.After a week,in a 400-member movement sample,there are 300 Males and 100 females.Whether can we make the conclusion that the ratio of female sports increase in golf course(=0.05).acceptance regionrejection regionsampling distribution of difference between two population parametersTest of difference between two population meanTest of difference between two population rateTest of difference between two population mean under the conditions of match samplesLarge samples(n1 30 and n2 30)condition，approximate normal distribution,namely:In Formula：1 standard deviation of population 12standard deviation of population 2n1the sample size of simple random sample from population 1n2the sample size of simple random sample from population 21 and 2 knowndistribution of distribution of standard deviation=1standard deviation=2Sampling distribution of Sampling distribution of Sampling distribution ofIn Formula:s1sample standard deviation of population 1 s2sample standard deviation of population 2 n1the sample size of simple random sample from population 1 n2the sample size of simple random sample from population 21 and 2unknownLarge samples(n1 30 and n2 30)condition，approximate normal distribution,namely:Small sample condition,there is t distribution of freedom n1+n2-2,namely:In Formula:s1sample standard deviation of population 1 s2sample standard deviation of population 2 n1the sample size of simple random sample from population 1 n2the sample size of simple random sample from population 21 and 2Unknown,but1=2 knownThere are two methods to be used to create the product with he important features of a tensile strength.Based on previous information that the first method produce products that its standard deviation of tensile strength is 8kg,the second method standard deviation is 10kg.sampling a random sample from the two methods produced products,the samples size were n1=32,n2=40,measured =50kg,=44kg.Asked the two methods produced an average tensile strength of the product is a significant difference(=0.05).A workshops study whether a product used the same time or not in two different assembly process.10 workers of a group use the first craftwork to assemble and install,required average time is 261 minutes,the sample standard deviation is 12 minutes.8 workers of another group use the second craftwork to assemble and install,required average time is 17.6 minutes,the standard deviation is 10.5 minutes.Known in two craftwork to assemble and install the product subject to the normal distribution,and 1=2，Do we think that the second method is better than the first method?Under large samples condition,:p1-p2 approximately subject to normal distribution,namely:Sampling distribution of p1-p2Young workers who come from two large enterprises participate in technical training to conduct the survey,the result as follows:Jia Chang:Survey 60,18 people took part in technical training.Yi Chang:survey 40,14 people took part in technical training.Based on the above findings can we think the number of Yi Chang workers that participate in technical training is higher than Jia Chang(=0.05).A manufacturing company,there are two methods to implement productive task for staff.In order to maximize output,the company tried to confirm which method has the shortest completed time.There are two optional programs to extract the samples.1、Independent samples program:a simple random sample of extracting workers,in which every worker use the method 1;another simple random sample of extracting workers,in which every worker use the method 2.Average difference test can adopt the test method under the independent samples conditions.2、Matching sample program：a simple random sample of extracting workers,every worker selects an method,then use another method,the order of two methods is random;every worker supply with a pair of data,one is method 1 and the other is method 2.worker Finished time of method 1（minute）Finished time of method 2（minute）Finished timedifference（di）1234566.05.07.06.26.06.45.45.26.55.96.05.80.6-0.20.50.30.00.6Matching sample dataMatching sample program,two types of production methods in conditions similar to those being tested(that is,by the same workers),so the program often than independent sample program has a smaller margin of error.This was mainly due to matching sampl