假設(shè)檢驗習(xí)題及答案

1、relationship, establi she d equivalent relati onship 14, and subje ct: a ppli cation problem 4-score s and percentage a ppli cation problem review conte nt overview a nswer s scores, a nd perce ntage applicati on pr oblem of key is: accordi ng to meani ng, 1 determine sta ndar d vol ume units "

2、1" 2 find associate "volume rate corresponds to" relationship, the n in -line sol ution. category fracti on multi plicati on w ord pr oblem score division applicati ons engi neeri ng problem problem xv, a subje ct: review of the measur ement of the am ount of capa city, measurement a

3、nd units of measurement of com mon units of measureme nt and their sig nifica nce i n rate 1, currency, le ngth, area, v olume, unit si ze, vol ume, weight a nd rate. omitted 2, commonly use d time unit s and t heir relationships. slightly with a measurement units zhijia n of of poly 1, and of metho

4、d 2, a nd poly method 3, a nd of method and poly meth od of relationshi p measureme nt dista nce of method 1, and tool mea sureme nt 2, and estimates 16, and subject: ge ometry preliminary k nowle dge 1-li ne and a ngle review conte nt line, a nd segment, and ray, a nd vertical , and parallel, a nd

5、a ngle angl e of classification slightly 17, and subje ct: geometry pr eliminary knowle dge 2-plane gra phi cs review conte nt triangle, a nd e dges shape d, a nd round, and fan axisymmetric graphi cs perimeter and are a com binati on graphics of area subje ct : preliminary knowledge 3-review of sol

6、i d content categ ory 1-d shape s are divided int o: cyli nder a nd cone 2, colum n is divi ded i nto: cuboi d, square 3, cone cone of the features of cuboids a nd cubes relati onship betwee n characteristi cs of cir cular cone is slig htly soli d surfa ce area and vol ume 1, size 2, table . 和第三章假設(shè)檢

7、驗3.2 一種元件 ,要求其使用壽命不低于1000（小時） ,現(xiàn)在從一批這種元件中隨機(jī)抽取 25 件,測得其壽命平均值為950（小時）；已知這種元件壽命聽從標(biāo)準(zhǔn)差10（0 小時） 的正態(tài)分布，試在顯著水平0.05 下確定這批元件是否合格；提出假設(shè)：h 0 :1000,h1 :1000構(gòu)造統(tǒng)計量：此問題情形屬于u檢驗，故用統(tǒng)計量：u= x00n此題中：x9500100n=2501000代入上式得：u=950-1000 100252.5拒絕域：v=uu1此題中：0.05u0.951.64即，uu0.95拒絕原假設(shè) h 0認(rèn)為在置信水平0.05下這批元件不合格；3.4 某批礦砂的五個樣品中鎳含量經(jīng)測

8、定為（% ）： 3.253.273.243.263.24設(shè)測定值聽從正態(tài)分布，問在0.01下能否接受假設(shè)，這批礦砂的鎳含量為提出假設(shè)：h 0 :103.25h 1 :10構(gòu)造統(tǒng)計量：此題屬于2未知的情形，可用t檢驗，即取檢驗統(tǒng)計量為：t=x0sn1此題中，x3.252,s=0.0117,n=5代入上式得：t=3.252-3.250.0117510.3419否定域為：v=t>tn11-此題中，q tt20.01,t0.995 44.604112接受 h 0 ,認(rèn)為這批礦砂的鎳含量為3.25；relationship, establi she d equivalent relati onsh

9、ip 14, and subje ct: a ppli cation problem 4-score s and percentage a ppli cation problem review conte nt overview a nswer s scores, a nd perce ntage applicati on pr oblem of key is: accordi ng to meani ng, 1 determine sta ndar d vol ume units "1" 2 find associate "volume rate corresp

10、onds to" relationship, the n in -line sol ution. category fracti on multi plicati on w ord pr oblem score division applicati ons engi neeri ng problem problem xv, a subje ct: review of the measur ement of the am ount of capa city, measurement a nd units of measurement of com mon units of measur

11、eme nt and their sig nifica nce i n rate 1, currency, le ngth, area, v olume, unit si ze, vol ume, weight a nd rate. omitted 2, commonly use d time unit s and t heir relationships. slightly with a measurement units zhijia n of of poly 1, and of method 2, a nd poly method 3, a nd of method and poly m

12、eth od of relationshi p measureme nt dista nce of method 1, and tool mea sureme nt 2, and estimates 16, and subject: ge ometry preliminary k nowle dge 1-li ne and a ngle review conte nt line, a nd segment, and ray, a nd vertical , and parallel, a nd a ngle angl e of classification slightly 17, and s

13、ubje ct: geometry pr eliminary knowle dge 2-plane gra phi cs review conte nt triangle, a nd e dges shape d, a nd round, and fan axisymmetric graphi cs perimeter and are a com binati on g raphics of area subje ct : preliminary knowledge 3-review of soli d content categ ory 1-d shape s are divided int

14、 o: cyli nder a nd cone 2, colum n is divi ded i nto: cuboi d, square 3, cone cone of the features of cuboids a nd cubes relati onship betwee n characteristi cs of cir cular cone is slig htly soli d surfa ce area and vol ume 1, size 2, table . 和3.5 確定某種溶液中的水分，它的10 個測定值 x0.452%, s0.035%,設(shè)總體為正態(tài)分布n,2 ,

15、 試在水平 5% 檢驗假設(shè)：i h 0 :0.5%h1 :0.5%ii h0 :0.04%h1 :0.0.4%i 構(gòu)造統(tǒng)計量：本文中未知，可用 t檢驗；取檢驗統(tǒng)計量為t=x0sn1此題中，x0.452%s=0.035%代入上式得：t=拒絕域為：0.452%-0.5%0.035%10-1-4.1143v=t >t 1-n1此題中，0.05n=10t0.95 91.8331t拒絕h 04.1143ii 構(gòu)造統(tǒng)計量：未知，可挑選統(tǒng)計量22 ns 2 0此題中，s0.035%n=1000.04%代入上式得：21否定域為：10 （0.035%）2（0.04%）27.6563v=此題中，22n122

16、1n10.95 916.919q221n1接受h 03.9 設(shè)總體 x :n , 4, x 1 ,k, x 16為樣本，考慮如下檢驗問題：relationship, establi she d equivalent relati onship 14, and subje ct: a ppli cation problem 4-score s and percentage a ppli cation problem review conte nt overview a nswer s scores, a nd perce ntage applicati on pr oblem of key is

17、: accordi ng to meani ng, 1 determine sta ndar d vol ume units "1" 2 find associate "volume rate corresponds to" relationship, the n in -line sol ution. category fracti on multi plicati on w ord pr oblem score division applicati ons engi neeri ng problem problem xv, a subje ct: r

18、eview of the measur ement of the am ount of capa city, measurement a nd units of measurement of com mon units of measureme nt and their sig nifica nce i n rate 1, currency, le ngth, area, v olume, unit si ze, vol ume, weight a nd rate. omitted 2, commonly use d time unit s and t heir relationships.

19、slightly with a measurement units zhijia n of of poly 1, and of method 2, a nd poly method 3, a ndof method and poly method of relationshi p measureme nt dista nce of m ethod 1, and tool mea sureme nt 2, and estimates 16, and subject: ge ometry preliminary k nowle dge 1-li ne and a ngle review conte

20、 nt line, a nd segment, and ray, a nd vertical , and parallel, a nd a ngle angl e of classification slightly 17, and subje ct: geometry pr eliminary knowle dge 2-plane gra phi cs review conte nt triangle, a nd e dges shape d, a nd round, and fan axisymmetric graphi cs perimeter and are a com binati

21、on graphics of area subje ct : preliminary knowledge 3-review of soli d content categ ory 1-d shape s are divided int o: cyli nder a nd cone 2, colum n is divi ded i nto: cuboi d, square 3, cone cone of the features of cuboids a nd cubes relati onship betwee n characteristi cs of cir cular cone is s

22、lig htly soli d surfa ce area and vol ume 1, size 2, table . 和h 0 :0h 1 :1i ii試證下述三個檢驗（否定域）犯第一類錯誤的概率同為v1=2x-1.645v 2 =1.502x2.125v3 =2x1.96或2x1.96通過運(yùn)算他們犯其次類錯誤的概率，說明哪個檢驗最好？=0.05解：i pxv h 00.05即， puxuu 0.975120.05這里 h 0 :0px2*1.960.05v12 x1.645p2 x1.645px01.6451.64511.645n=1-0.95=0.05v 21.502 x2.1251.

23、50x02.120p v2 h 0n2.2151.500.980.930.05v32 x1.96或2 x1.962 x1.96x01.96p v3（ ii ）h 0 =1-p2 xn1.96211.960.05犯其次類錯誤的概率=p-v h1v1 :1 =p 2 x1.6451relationship, establi she d equivalent relati onship 14, and subje ct: a ppli cation problem 4-score s and percentage a ppli cation problem review conte nt overv

24、iew a nswer s scores, a nd perce ntage applicati on pr oblem of key is: accordi ng to meani ng, 1 determine sta ndar d vol ume units "1" 2 find associate "volume rate corresponds to" relationship, the n in -line sol ution. category fracti on multi plicati on w ord pr oblem score

25、division applicati ons engi neeri ng problem problem xv, a subje ct: review of the measur ement of the am ount of capa city, measurement a nd units of measurement of com mon units of measureme nt and their sig nifica nce i n rate 1, currency, le ngth, area, v olume, unit si ze, vol ume, weight a nd

26、rate. omitted 2, commonly use d time unit s and t heir relationships. slightly with a measurement units zhijia n of of poly 1, and of method 2, a nd poly method 3, a nd of method and poly meth od of relationshi p measureme nt dista nce of method 1, and tool mea sureme nt 2, and estimates 16, and sub

27、ject: ge ometry preliminary k nowle dge 1-li ne and a ngle review conte nt line, a nd segment, and ray, a nd vertical , and parallel, a nd a ngle angl e of classification slightly 17, and subje ct: geometry pr eliminary knowle dge 2-plane gra phi cs review conte nt triangle, a nd e dges shape d, a n

28、d round, and fan axisymmetric graphi cs perimeter and are a com binati on g raphics of area subje ct : preliminary knowledge 3-review of soli d content categ ory 1-d shape s are divided int o: cyli nder a nd cone 2, colum n is divi ded i nto: cuboi d, square 3, cone cone of the features of cuboids a

29、 nd cubes relati onship betwee n characteristi cs of cir cular cone is slig htly soli d surfa ce area and vol ume 1, size 2, table . 和=px10.35510.3550.36v2 :2n1p 1.502x2.1251=1-p3.50x14.125n=1-4.125+3.50=1v3 :3p2x1.961=p0.04x13.96n=3.96-0.04=0.99996092-0.516=0.48396092v1顯現(xiàn)其次類錯誤的概率最小，即v1最好；3.10 一骰子投擲

30、了 120 次，得到以下結(jié)果：點數(shù)123456顯現(xiàn)次數(shù)232621201515問這個骰子是否勻稱？0.05解：此題原假設(shè)為：h10 : pi6i=1,2,l ,6這里 n=120,npi20此題采納的統(tǒng)計量為pearson2統(tǒng)計量即，2kni i 12npi npi代入數(shù)據(jù)為：k22222nii 1npi npi（ 23-20 ） （ 26-20 ）l20（ 15-20 ） =4.8relationship, establi she d equivalent relati onship 14, and subje ct: a ppli cation problem 4-score s and

31、percentage a ppli cation problem review conte nt overview a nswer s scores, a nd perce ntage applicati on pr oblem of key is: accordi ng to meani ng, 1 determine sta ndar d vol ume units "1" 2 find associate "volume rate corresponds to" relationship, the n in -line sol ution. cat

32、egory fracti on multi plicati on w ord pr oblem score division applicati ons engi neeri ng problem problem xv, a subje ct: review of the measur ement of the am ount of capa city, measurement a nd units of measurement of com mon units of measureme nt and their sig nifica nce i n rate 1, currency, le

33、ngth, area, v olume, unit si ze, vol ume, weight a nd rate. omitted 2, commonly use d time unit s and t heir relationships. slightly with a measurement units zhijia n of of poly 1, and of method 2, a nd poly method 3, a ndof method and poly method of relationshi p measureme nt dista nce of m ethod 1

34、, and tool mea sureme nt 2, and estimates 16, and subject: ge ometry preliminary k nowle dge 1-li ne and a ngle review conte nt line, a nd segment, and ray, a nd vertical , and parallel, a nd a ngle angl e of classification slightly 17, and subje ct: geometry pr eliminary knowle dge 2-plane gra phi

35、cs review conte nt triangle, a nd e dges shape d, a nd round, and fan axisymmetric graphi cs perimeter and are a com binati on graphics of area subje ct : preliminary knowledge 3-review of soli d content categ ory 1-d shape s are divided int o: cyli nder a nd cone 2, colum n is divi ded i nto: cuboi

36、 d, square 3, cone cone of the features of cuboids a nd cubes relati onship betwee n characteristi cs of cir cular cone is slig htly soli d surfa ce area and vol ume 1, size 2, table . 和221 （ k-1） =20.9（525 ） =11.071由于1 （ k-1） 所以接受 h 0即認(rèn)為這個是勻稱的；3.11 某電話站在一小時內(nèi)接到電話用戶的呼吁次數(shù)按每分鐘記錄的如下表：0123456>=7816171

37、06210呼吸次數(shù)頻數(shù)試問這個分布能看作為泊松分布嗎？（=0.05 ）解：檢驗問題為：k eh0 : pxk k.參數(shù)為已知 的最大似然估量xn p081* 16l6*17*0l260606060021ppx0p2px1ppx2ppx3ppx4ppx5ppx62 ee 20.0.13531222 e2* e 1.220.27072 e32.2* e 20.27073242 e1.5* e 23.0.20304252 e2 * e 20.09024.3522 e46* e 20.03615.15622 e47* e 20.01206.45p8px71px60k22222ninpi 860*0.13531660*0.2707l160*0.0120i 1npi60*0.135360*0.270760*0.0120= 0.614522由于1 （ k-1） =1q22 （ k-1 ）0