HypothesisTesting统计学假设检验课件.ppt
- 【下载声明】
1. 本站全部试题类文档,若标题没写含答案,则无答案;标题注明含答案的文档,主观题也可能无答案。请谨慎下单,一旦售出,不予退换。
2. 本站全部PPT文档均不含视频和音频,PPT中出现的音频或视频标识(或文字)仅表示流程,实际无音频或视频文件。请谨慎下单,一旦售出,不予退换。
3. 本页资料《HypothesisTesting统计学假设检验课件.ppt》由用户(晟晟文业)主动上传,其收益全归该用户。163文库仅提供信息存储空间,仅对该用户上传内容的表现方式做保护处理,对上传内容本身不做任何修改或编辑。 若此文所含内容侵犯了您的版权或隐私,请立即通知163文库(点击联系客服),我们立即给予删除!
4. 请根据预览情况,自愿下载本文。本站不保证下载资源的准确性、安全性和完整性, 同时也不承担用户因使用这些下载资源对自己和他人造成任何形式的伤害或损失。
5. 本站所有资源如无特殊说明,都需要本地电脑安装OFFICE2007及以上版本和PDF阅读器,压缩文件请下载最新的WinRAR软件解压。
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- HypothesisTesting 统计学 假设检验 课件
- 资源描述:
-
1、HypothesisTesting统计学假设检验1Hypothesis Testing9.1Null and Alternative Hypotheses and Errors in Testing9.2z Tests about a Population with known s9.3t Tests about a Population with unknown s2Hypothesis testing-1Researchers usually collect data from a sample and then use the sample data to help answer que
2、stions about the population.Hypothesis testing is an inferential statistical process that uses limited information from the sample data as to reach a general conclusion about the population.3 A hypothesis test is a formalized procedure that follows a standard series of operations.In this way,researc
3、hers have a standardized method for evaluating the results of their research studies.4Hypothesis testing-25The basic experimental situation for using hypothesis testing is presented here.It is assumed that the parameter is known for the population before treatment.The purpose of the experimentis to
4、determine whether or not the treatment has an effect.Is the population mean after treatment the same as or different from the mean before treatment?A sample is selected from the treated population to help answer this question.Procedures of hypothesis-testing61.First,we state a hypothesis about a pop
5、ulation.Usually the hypothesis concerns the value of a population parameter.For example,we might hypothesize that the mean IQ for UIC students is =110.2.Next,we obtain a random sample from the population.For example,we might select a random sample of n=100 UIC students.3.Finally,we compare the sampl
6、e data with the hypothesis.If the data are consistent with the hypothesis,we will conclude that the hypothesis is reasonable.But if there is a big discrepancy between the data and the hypothesis,we will decide that the hypothesis is wrong.Null and Alternative Hypotheses The null hypothesis,denoted H
7、0,is a statement of the basic proposition being tested.It generally represents the status quo(a statement of“no effect”or“no difference”,or a statement of equality)and is not rejected unless there is convincing sample evidence that it is false.The(scientific or)alternative hypothesis,denoted Ha(or H
8、1),is an alternative(to the null hypothesis)statement that will be accepted only if there is convincing sample evidence that it is true.These two hypotheses are mutually exclusive and exhaustive.78Determined by the level of significance or the alpha level9Alpha level of.05-the probability of rejecti
9、ng the null hypothesis when it is true is no more than 5%.Z10The locations of the critical region boundaries for three different levels of significance11Example:Alcohol appears to be involved in a variety of birth defects,including low birth weight and retarded growth.A researcher would like to inve
10、stigate the effect of prenatal alcohol on birth weight.A random sample of n=16 pregnant rats is obtained.The mother rats are given daily doses of alcohol.At birth,one pup is selected from each litter to produce a sample of n=16 newborn rats.The average weight for the sample is 15 grams.The researche
11、r would like to compare the sample with the general population of rats.It is known that regular newborn rats(not exposed to alcohol)have an average weight of m=18 grams.The distribution of weights is normal with sd=4.12H0:=18 131.State the hypothesesThe null hypothesis states that exposure to alcoho
12、l has no effect on birth weight.The alternative hypothesis states that alcohol exposure does affect birth weight.2.Select the Level of Significance(alpha)levelWe will use an alpha level of.05.That is,we are taking a 5%risk of committing a Type I error,or,the probability of rejecting the null hypothe
13、sis when it is true is no more than 5%.3.Set the decision criteria by locating the critical region14Alpha level of.05-the probability of rejecting the null hypothesis when it is true is no more than 5%.Z154.COLLECT DATA and COMPUTE SAMPLE STATISTICSThe sample mean is then converted to a z-score,whic
14、h is our test statistic.316/41815n/0sXz5.Arrive at a decisionReject the null hypothesis Hypothesis TestingDo not reject nullReject null and accept alternateStep 5:Take a sample,arrive at a decisionStep 4:Formulate a decision ruleStep 3:Identify the test statisticStep 2:Select a level of significance
15、Step 1:State null and alternate hypothesesAlternative Hypothesis H1:A statement that is accepted if H0 is falseWithout“=”signSay,“2”or“2”Null Hypothesis H0:A statement about the value of a population parameter(and s s).With“=”signSay,“=2”or“2”17Three possibilities regarding meansH0:=0H1:=0H0:0H0:0H1
16、:0The null hypothesis always contains equality.3 hypotheses about means18a constantMeasures the max probability of rejecting a true null hypothesisH0 is actually true but you reject it(false positive).H0 is false but you accept it(false negative).19too highLevel of Significance:the maximum allowable
17、 probability of making a type I error Researcher Null Accepts RejectsHypothesis Ho HoHo is trueHo is falseCorrectdecisionType I error(a)(Critical zComputed z Critical zOr Computed z Critical z.01.65Do notrejectProbability=.95Region of rejectionProbability=.05Critical valueIf H0:0 is true,it is very
18、unlikely that the computed z value is so large.2526H0:0Computed z 1.9631Step 4:ConcludeWe can see that z=1.897 1.96,thus our test statistic is not in the rejection region.Therefore we fail to reject the null hypothesis.We cannot conclude anything statistically significant from this test,and cannot t
19、ell the insurance company whether or not they should be concerned about their current policies.Example One Tailed(Upper Tailed)32Trying to encourage people to stop driving to campus,the university claims that on average it takes people 30 minutes to find a parking space on campus.John does not think
20、 it takes so long to find a spot.He calculated the mean time to find a parking space on campus for the last five times and found it to be 20 minutes.Assuming that the time it takes to find a parking spot is normally distributed,and that the population standard deviation=6 minutes,perform a hypothesi
21、s test with level of significance alpha=0.10 to see if his claim is correct.Example:One Tailed(Lower Tailed)33Step 1:Set the null and alternative hypothesesExample:One Tailed(Lower Tailed)Step 2:Calculate the test statisticStep 3:Set Rejection RegionLooking at the picture below,we need to put all of
22、 alpha in the left tail.Thus,R:Z -1.28 34Example:One Tailed(Lower Tailed)Step 4:ConcludeWe can see that z=-3.727 -1.28,thus our test statistic is in the rejection region.Therefore we reject the null hypothesis in favor of the alternative.We conclude that the mean is significantly less than 30,thus J
23、ohn has proven that the mean time to find a parking space is less than 30.35Example:Two TailedA sample of 40 sales receipts from a grocery store has mean =$137 and population standard deviation=$30.2.Use these values to test whether or not the mean in sales at the grocery store are different from$15
展开阅读全文