【正文】 決定顯著水平，找到臨界值 ? Calculate the t statistic based on the sample data 根據(jù)樣本數(shù)據(jù)計算 t 統(tǒng)計量 ? Compare the t statistic with the critical value to decide whether to reject the null ? 比較 t 值與臨界值，決定是否拒絕零假設(shè)。我們是否應(yīng)當拒絕零假設(shè)？ ? Committing to a significance level ahead of time can hide useful information about the oute of a hypothesis test. 提前確定顯著水平可能會隱藏關(guān)于假設(shè)檢驗的一些有用信息。當 a?， c是 nk1自由度的 t分布的 。 Useful information about pvalues 一些關(guān)于 p值的信息 ? Because it is a probability, its range is between 0 and 1. 由于這是一個概率，其取值范圍在 0， 1之間 ? Small p values are evidence against the null, large p values provide little evidence against the null. 小 p值提供了拒絕零假設(shè)的證據(jù)，大 p值不能提供證據(jù)拒絕零假設(shè)。 ? Commonly specified significance levels: , . If it equals , it means the researcher is willing to falsely reject the null at 5% of the time. 通常設(shè)定的限制性水平為： ,。 ? Assumption (Normality): Assume that u is independent of x1, x2,…, xk and u is normally distributed with zero mean and variance s2: u ~ Normal(0,s2) 假設(shè) （正態(tài)）：假設(shè) u與 x1, x2,…, xk獨立，且 u服從均值為 0，方差為 s2的正態(tài)分布。 Theorem Normal Sampling Distributions 定理 正態(tài)樣本分布 ? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?是誤差的線性組合服從正態(tài)分布，因為它故量的樣本值有假設(shè)下，條件于解釋變在jj?0 , 1N o r m a l ~ ??,?,N o r m a l ~?C L Me r r o r s t h eofn c o m b i n a t i ol i n e ar a isi t b e c a u s en o r m a l l y dd i s t r i b u t e is ?0 , 1N o r m a l ~ ?? t h atso ,?,N o r m a l ~? st v ar i a b l ei n d e p e n d e n t h e of v a l u ess am p l e o n t h e lc o n d i t i o n a s,a s s u m p t i o n C L M U n d er t h ebbbbbbbbbbbbbbjjjjjjjjjjjjsdV a rsdV a r?? Testing Hypotheses about a Single Population Parameter: the ttest 對單個總體參數(shù)的假設(shè)檢驗： t檢驗 ? Consider a population model () which satisfies the CLM assumptions. We now study how to test hypotheses about a particular 考慮總體中滿足 CLM的模型 我們現(xiàn)在研究如何對一個特定的 進行假設(shè)檢驗 0 1 1 ... kky x x ub b b? ? ? ? ?jb0 1 1 ... kky x x ub b b? ? ? ? ?jbBackground Review 背景知識回顧 ? The hypothesis to be tested is called the null hypothesis. 被檢驗的假設(shè)稱為零假設(shè) ? Hypothesis testing entails using data to pare the null hypothesis with a second hypothesis, ., the alternative hypothesis. 假設(shè)檢驗利用數(shù)據(jù)將零假設(shè)和另一個假設(shè)（替代假設(shè)）進行比較 Background Review 背景知識回顧 ? The alternative hypothesis specifies what is true if the null hypothesis is not. 替代假設(shè)給出在零假設(shè)不成立時的真實情況。 ? The set of values of the test statistic for which the test rejects the null is the rejection region, and the values of the test statistic for which it does not reject the null is the acceptance region. ? 假設(shè)檢驗中，使得零假設(shè)被拒絕的檢驗統(tǒng)計量的取值范圍稱為 拒絕域 ，使得零假設(shè)不能被拒絕的檢驗統(tǒng)計量的取值范圍成為 接受域 。由于 ，故在 1%顯著水平下拒絕零假設(shè)。由于 ，我們不能拒絕零