英語翻譯路橋081高彥召

1、7.8 Hypothesis Testing 7.8 假設(shè)測試路橋081 高彥召20082201301 Very often traffic engineers must make a decision based on sample information. For example, is a traffic control effective or not? To test this, we formulate a hypothesis,Ha, called the null hypothesis and then try to disprove it.The null hypothesi

2、s is formulated so that there is no difference or no change, and then the opposite hypothesisis called the alternative hypothesis, Hj 很久以前，交通工程師們就必須根據(jù)樣本的信息做出決定。例如：交通控制是否起作用？為了檢驗(yàn)它，我們構(gòu)想出一個(gè)假設(shè)HO。叫做失效的假設(shè)，然后試著推翻它 。這個(gè)失效的假設(shè)是這樣設(shè)想的：他沒有不同和變化，所以他的反面的假設(shè)叫做可選擇的假設(shè)H1When testing a hypothesis, it is possible to make

3、two types of errors: (1) We could reject a hypothesis that should be accepted (e.g., sayan effective control is not effective). This is called a Type I error. The probability of making a Type I error is given the variable name,0'.(2) We could accept a false hypothesis (e.g., sayan ineffective co

4、ntrol is effective). This is called a Type II error. A Type II error is given the variable name f3."當(dāng)測試一個(gè)假說，它有可能有兩種類型的錯(cuò)誤：（1）我們可以拒絕一個(gè)本應(yīng)該被接受的假設(shè)（例如，說有效的控制是無效的）。這就是所謂的I型錯(cuò)誤。用變量名a表示第一種事件發(fā)生的可能性（2）我們可以成立一個(gè)虛假的假設(shè)（例如，無效的控制是有效的）。這就是所謂的II型錯(cuò)誤用變量名b表示第二個(gè)事件的可能性。Consider this example: An auto inspection program

5、is going to be applied to 100,000 vehicles, of which 10,000 are "unsafe" and the rest are "safe." Of course, we do not know which cars are safe and which are unsafe."考慮下面的例子：一個(gè)自動(dòng)檢查計(jì)劃將被應(yīng)用到100,000輛車，其中10000是“不安全”，其余的是“安全”。當(dāng)然，我們不知道哪輛車是安全的，哪些是不安全的。"We have a test procedure,

6、 but it is not perfect, due to the mechanic and test equipment used. We know that 15% of the unsafe vehicles are determined to be safe, and 5% of the safe vehicles are determined to be unsafe,as seen in Figure 7.6."我們有一個(gè)測試程序，但它并非十全十美，由于在機(jī)械和測試設(shè)備使用。我們知道，15是不安全的車輛確定為安全，和5的車輛安全確定為不安全的，就像在圖7.6。"

7、;We would define: Ho: The vehicle being tested is "safe," and Hi: the vehicle being tested is "unsafe." The Type I error, rejecting a true null hypothesis (false negative), is labeling a safe vehicle as "unsafe." The probability of this is called the level of significan

8、ce, a, and in this case a = 0.05. The Type II error, failing to reject a false null hypothesis (false positive), is labeling an unsafe vehicle as "safe." The probability of this, b is 0.15. In general, for a given test procedure, one can reduce Type I error only by living with a higher Typ

9、e II error, or vice versa."我們將定義：H0：被測試的車輛是“安全”和Hi：被測試的車輛是“不安全”。第一類錯(cuò)誤，拒絕真正的無效假設(shè)（錯(cuò)誤的觀點(diǎn)），作為安全汽車“不安全”的標(biāo)簽。A作為這種水平的概率，在這種情況下a= 0.05。第二類錯(cuò)誤，不拒絕無效假設(shè)（錯(cuò)誤的態(tài)度），是標(biāo)示為不安全的車輛為“安全”。這個(gè)概率，b=0.15。一般來說，給定的測試程序，一個(gè)人可以減少誤差只有I型生活有較高的第二類錯(cuò)誤，反之亦然。"7.8.1 Before-and-After Tests with Two Distinct Choices在得到兩個(gè)不同截然不同的結(jié)果前后

10、In a number of situations, there are two clear and distinct choices, and the hypotheses seem almost self-defining:"在許多情況下，有兩個(gè)清晰的和獨(dú)特的選擇，并假設(shè)看起來幾乎是自定義：" Auto inspection (acceptable, not acceptable) Disease (have the disease, don't) Speed reduction of 5 mph (it happened, it didn't) Acc

11、ident reduction of 10% (it happened, it didn't) Mode: shift by five percentage points (it happened,it didn't)"自動(dòng)檢查（接受，不接受） 病害（有病害，不）以每5英里的速度減少（它發(fā)生，它沒有）事故以10速率減少（它發(fā)生，它沒有）模式：由五個(gè)百分點(diǎn)（它的發(fā)生，它沒有）"Of course, there is the distinction between the real truth (reality, unknown to us) and the d

12、ecision we make, as already discussed and related to Type I and Type II errors. That is, we can decide that some cars in good working order need repairing and we can decide thatsome unsafe cars do not need repairing."當(dāng)然，還有的真正區(qū)別真理（現(xiàn)實(shí)中，我們未知的）和我們所做的決定，正如已經(jīng)討論過的相關(guān)的I型和II型錯(cuò)誤。也就是說，我們可以決定在一些好車需要維修的工作秩序，

13、我們可以決定一些不安全的車不進(jìn)行修葺工程。"There is also the distinction that people may not want to reduce the issue to a binary choice or might not be able to do so. For instance, if an engineer expects a 10% decrease in the accident rate, should we test "Ho: no change" against "Hi: 10% decrease&qu

14、ot; and not allow the possibility of a 5% change? Such cases are addressed in the next section. For the present section, we will concentrate on binary choices"也有區(qū)別，人們可能不希望減少這個(gè)雙重的的選擇或者不能。例如，如果一個(gè)工程師預(yù)計(jì)，事故率降低10，我們應(yīng)該測試“H0：不改變”或者反對(duì)“H1：減少10”，而不是允許有5的變化的可能性？這種情況將在下一節(jié)討論。對(duì)于本節(jié)中，我們將集中于一對(duì)問題的選擇"Applicat

15、ion: Travel Time Decrease "應(yīng)用：旅游時(shí)間縮短"Consider a situation in which the existing travel time on a given route is known to average 60 minutes, and experience has shown the standard deviation to be about 8 minutes. An "improvement" is recommended that is expected to reduce the true

16、mean travel time to 55 minutes"考慮一個(gè)情況，即有一個(gè)六十分鐘的路車，經(jīng)歷告訴我更具有八分鐘的誤差。 “改善”的建議是預(yù)計(jì)將減少旅行時(shí)間到55分鐘"This is a rather standard problem, with what is now a fairly standard solution. The logical development of the solution follows."這是一個(gè)比較標(biāo)準(zhǔn)的問題，也是一個(gè)相當(dāng)標(biāo)準(zhǔn)的解決方案。邏輯的提高方案隨著事態(tài)的發(fā)展。The first question we might ask ourselves is whether we can consider the mean and standard deviation of the initial distribution to be truly known or whether they must be estimated. Actually, we will avoid this question simp