1、HYPOTHESIS TESTING,REDGEMANUIDAHO.EDU OFFICE: +1-208-885-4410,To start our presentation well ask 3 questions.,Why?,What?,How?,why shoud we do Hypothesis-testing?,For the probability distribution or the unknown parameter of population,many hypothesises are made in econometrics. Hypothesis-testing is
2、a method of using sampling information to make sure whether the hypothesises are reasonable.In a word,we always estimate the population by using sample information,but weather its reliable depends on hypothesis testing, so we need hypothesis testing,Whats HYPOTHESIS TESTING ?,Hypothesis Testing is a
3、n organized and systematic way to confirm whether the stated assertion (or hypothesis) is statistically valid or not within a defined confidence interval.,Types of Hypothesis Null hypothesis. The null hypothesis, denoted by H0, is usually the hypothesis that sample observations result purely from ch
4、ance. Alternative hypothesis. The alternative hypothesis, denoted by H1 or Ha, is the hypothesis that sample observations are influenced by some non-random cause.,HYPOTHESIS TESTING,Generally, null hypothesis and alternative hypothesis that based on actual application problem should be sure properly
5、. From a logical point of view，we usually think that null hypothesis is a high probability event,so we often asumed that the null hypothesis is true.,The elements of Hypothesis testing is that under a certain statistic hypothesis premise,if there was a small probability event, we have reasons to dou
6、bt the authenticity of the hypothesis,so that we refuse to accept the hypothesis.,Giving a significance level (which is normally 5% or 1%) and basing on the sampling distribution of mentioned above,the next is to determine the critical value when the null hypothesis is true,and the critical value ca
7、n constitute acceptance region and rejection region.,if,we can refuse H0,else,accept it,Type I and Type II error,Type I error : Suppose we test the null hypothesis that is true and at a significance level(suppose it is 5% here)reject the null hypothesis. It is possible that we will have incorrectly
8、rejected the null hypothesis.This mistake is called a Type I error. Type II error: We also would have accepted the null hypothesis when it was in fact false .This mistake ,called a Type II error.,P-value,The strength of evidence in support of a null hypothesis is measured by the P-value. Suppose the
9、 test statistic is equal to S, P is the probability of observing a test statistic as extreme as S.Assuming the null hypothesis is true, if the P-value is less than the significance level, we reject the null hypothesis.,Types of Test,One-tailed test - the alternate hypothesis H1 is one-sided and we t
10、est whether the test statistic falls in the critical region on only one side of the distribution Two-tailed test - the alternate hypothesis H1 is formulated to test for difference in either direction, i.e., for either an increase or a decrease in the random variable.,How to carry on hypothesis testi
11、ng,When we collet the sample information,and got the parameter estimates,the next is begain our hypothesis testing ,that is our third questions : how to carry on hypothesis testing.,STEPS IN HYPOTHESIS TESTING,State the Null Hypothesis Specify an appropriate Alternative Hypothesis Set Level of Signi
12、ficance Determine an appropriate Test Statistic for the test Define the Critical Region Compute for the Test Statistic Draw corresponding conclusion,Example,A department store manager determines that a new billing system will be cost-effective only if the mean monthly account is more than $170.A ran
13、dom sample of 400 monthly accounts is drawn, for which the sample mean is $178. The accounts are approximately normally distributed with a standard deviation of $65.,The system will be cost effective if the mean account balance for all customers is greater than $170. We express this belief as a our
14、research hypothesis, that is:H1: 170 (this is what we want to determine) Thus, our null hypothesis becomes:H0: = 170 (this specifies a single value for the parameter of interest) Actually H0: 170,The rejection region is a range of values such that if the test statistic falls into that range, we deci
15、de to reject the null hypothesis in favor of the alternative hypothesis.,At a 5% significance level (i.e. =0.05), we get all in one tailSince our sample mean (178) is greater than the critical value we calculated (175.35), we reject the null hypothesis in favor of H1.OR,HYPOTHESIS TESTING,If the p-v
16、alue is less than 1%, there is overwhelming evidence that supports the alternative hypothesis. If the p-value is between 1% and 5%, there is a strong evidence that supports the alternative hypothesis. If the p-value is between 5% and 10% there is a weak evidence that supports the alternative hypothe
17、sis. If the p-value exceeds 10%, there is no evidence that supports the alternative hypothesis. We observe a p-value of .0069, hence there is overwhelming evidence to support H1: 170.,HYPOTHESIS TESTING,Example 2: In a trial a jury must decide between two hypotheses. The null hypothesis is H0: The d
18、efendant is innocent (null hypothesis)The alternative hypothesis or research hypothesis isH1: The defendant is guilty (alternative hypothesis)The jury does not know which hypothesis is true. They must make a decision on the basis of evidence presented.,Example: In a trial a jury must decide between
19、two hypotheses. The null hypothesis is H0: The defendant is innocent (null hypothesis)The alternative hypothesis or research hypothesis isH1: The defendant is guilty (alternative hypothesis)The jury does not know which hypothesis is true. They must make a decision on the basis of evidence presented.
20、,HYPOTHESIS TESTING,Example,In the language of statistics convicting the defendant is called rejecting the null hypothesis in favor of the alternative hypothesis. That is, the jury is saying that there is enough evidence to conclude that the defendant is guilty (i.e., there is enough evidence to sup
21、port the alternative hypothesis). If the jury acquits it is stating that there is not enough evidence to support the alternative hypothesis. Notice that the jury is not saying that the defendant is innocent, only that there is not enough evidence to support the alternative hypothesis. That is why we
22、 never say that we accept the null hypothesis, although most people in industry will say “We accept the null hypothesis”,Two possible errors:A Type I error occurs when we reject a true null hypothesis. That is, a Type I error occurs when the jury convicts an innocent person.A Type II error occurs wh
23、en we dont reject a false null hypothesis accept the null hypothesis. That occurs when a guilty defendant is acquitted.,Example,A Type I error occurs when we reject a true null hypothesis(i.e. Reject H0 when it is TRUE) A Type II error occurs when we dont reject a false null hypothesis (i.e. Do NOT reject H0 when it is FALSE),Example,Type I Error,Right decision,Right decision,Type II Error,Decision,H0 is true,H1 is true,Reject H0 Dont reject H0,HYPOTHESIS TESTINGthe end,
