Chapter 10: H at alpha of.05. Hypothesis Testing: Additional Topics

Transcription

1 Chapter 10: pothei Tetig: Additioal Topic 10.1 = 5 paired obervatio with ample mea of 50 ad 60 for populatio 1 ad. Ca ou reject the ull hpothei at a alpha of.05 if a. d = 0, : 0 1 0; : 1 1 0; 10 0 t = -.500, p-value =.990. Do ot reject at alpha of.05. Paired T-Tet ad CI N Mea StDev SE Mea Differece % lower boud for mea differece: T-Tet of mea differece = 0 (v > 0): T-Value = -.50 P-Value = b. d = 30, : 1 0 0; : 1 1 0; 10 0 t = -1.67, p-value = Do ot reject at alpha of.05 Paired T-Tet ad CI N Mea StDev SE Mea Differece % lower boud for mea differece: -0.7 T-Tet of mea differece = 0 (v > 0): T-Value = P-Value = c. d = 15, : 1 0 0; : 1 1 0; 10 0 t = -3.33, p-value = Do ot reject at alpha of.05 Paired T-Tet ad CI N Mea StDev SE Mea Differece % lower boud for mea differece: T-Tet of mea differece = 0 (v > 0): T-Value = P-Value = d. d = 40, : 1 0 0; : 1 1 0; 10 0 t = -1.5, p-value = Do ot reject at alpha of.05 Copright 013 Pearo Educatio, Ic. publihig a Pretice all. 10-1

2 10- Statitic for Buie & Ecoomic, 7 th editio Paired T-Tet ad CI N Mea StDev SE Mea Differece % lower boud for mea differece: T-Tet of mea differece = 0 (v > 0): T-Value = -1.5 P-Value = = 5 paired obervatio with tadard deviatio of the differece betwee ample mea = 5. Ca ou reject the ull hpothei at a alpha of.05 if a. The ample mea are 56 ad 50, : 0 1 0; : 1 1 0; 6 0 t = 1., p-value = Do ot reject 0 at alpha of.05 Paired T-Tet ad CI N Mea StDev SE Mea Differece % upper boud for mea differece: T-Tet of mea differece = 0 (v < 0): T-Value = 1.0 P-Value = b. The ample mea are 59 ad 50, : 1 0 0; : 1 1 0; 9 0 t = 1.8, p-value = Do ot reject at alpha of.05 Paired T-Tet ad CI N Mea StDev SE Mea Differece % upper boud for mea differece: T-Tet of mea differece = 0 (v < 0): T-Value = 1.80 P-Value = c. The ample mea are 56 ad 48, : 1 0 0; : 1 1 0; 8 0 t = 1.60, p-value =.939. Do ot reject at alpha of.05 Paired T-Tet ad CI N Mea StDev SE Mea Differece % upper boud for mea differece: T-Tet of mea differece = 0 (v < 0): T-Value = 1.60 P-Value = d. The ample mea are 54 ad 50, : 1 0 0; : 1 1 0; 4 0 t = 0.8, p-value =.784. Do ot reject at alpha of.05 Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

3 Chapter 10: pothei Tetig: Additioal Topic 10-3 Paired T-Tet ad CI N Mea StDev SE Mea Differece % upper boud for mea differece: 1.55 T-Tet of mea differece = 0 (v < 0): T-Value = 0.80 P-Value = Let Germe Bak ad Great Britai Bak : 0; : 0; t =.04, p-value =.043. Reject at alpha level i ece of 4.3% Paired T-Tet ad CI N Mea StDev SE Mea Differece % CI for mea differece: ( , ) T-Tet of mea differece = 0 (v ot = 0): T-Value =.04 P-Value = Let Iitial urba home ellig price; Urba home ellig price over time Urba home ellig price i Atlata, Chicago, Dalla, ad Oaklad, : 0; : 0; 0 1 Paired T-Tet ad CI: Sale 1 Price, Sale Price Paired T for Sale 1 Price - Sale Price N Mea StDev SE Mea Sale 1 Price Sale Price Differece % lower boud for mea differece: -944 T-Tet of mea differece = 0 (v > 0): T-Value = P-Value = Sice, p-value i equal to 1.000, we do ot reject the ull hpothei. b) Urba home ellig price i Atlata, : 0; : 0; t = , p-value = Do ot reject at a level of alpha. Paired T for Sale 1 Price - Sale Price N Mea StDev SE Mea Sale 1 Price Sale Price Differece % lower boud for mea differece: T-Tet of mea differece = 0 (v > 0): T-Value = P-Value = Sice, p-value i equal to 1.000, we do ot reject the ull hpothei. Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

4 10-4 Statitic for Buie & Ecoomic, 7 th editio 10.5 Let took the preparatio coure; did ot take the preparatio coure : 0; : 0; 0 1 reject 0 if t (5,.05) > t =.665. Reject at the 5% level 10.6 Let Proce 1; Proce z a. Reject 0 if D z Do ot reject 0 at alpha of.05. b. Reject 0 if z 0 z Reject 0 at alpha of.05. c. Reject 0 if z z Do ot reject 0 at alpha of.05.. For.05, z z For.05, z z For.05, z z Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

5 Chapter 10: pothei Tetig: Additioal Topic 10-5 d. Reject 0 if z 15 z Do ot reject 0 at alpha of.05.. For.05, z z Let Proce 1; Proce t, a. Reject 0 if. For the give data, t, t59, p ( 1) ( 1) (4)(30) (35)(8) ( ) (5 36 ) t p 5 36 Do ot reject 0 at alpha of.05. b. Reject 0 if p, p t ( 1) ( 1) (4)() (35)(33) ( ) (5 36 ) t p 5 36 Do ot reject 0 at alpha of For the give data, t, t59, Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

6 10-6 Statitic for Buie & Ecoomic, 7 th editio c. Reject 0 if p, p t ( 1) ( 1) (4)(30) (35)(4) ( ) (5 36 ) t p 5 36 Do ot reject 0 at alpha of.05. d. Reject 0 if p, p t ( 1) ( 1) (4)(15) (35)(36) ( ) (5 36 ) t p 5 36 Do ot reject 0 at alpha of.05.. For the give data, t, t59, For the give data, t, t59, Let male fiacial aalt; female fiacial aalt : 0; : 0; z (19.13) /151 (1.) /108 = Reject 0 at all commo level of alpha 10.9 Let Britih etrepreeur; Britih corporate maager : 0; : 0; z (1.3) /15 (.53) / 86 = Reject 0 at all commo level of alpha. Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

7 Chapter 10: pothei Tetig: Additioal Topic Let tudet who vote; tudet who do ot vote : 0; : 0; z (.64) /114 (.56) /13 = , p-value = [1-F Z (1.0)] = [ ] =.3078 Therefore, reject 0 at level of alpha i ece of 30.78% Let auditor ued the cah-flow iformatio; auditor ot uig the cah-flow iformatio : 0; : 0; 0 1 ( 1) ( 1) t p p = = 35(.93) 35(7.56) t 70 (1.8995)=.0308; p-value = (.0308) = Reject 0 at level i ece of 6.16% = = Let proectue i which ale forecat were dicloed; proectue i which ale earig forecat were ot dicloed Aumig both populatio are ormal with equal variace: : 0; : 0; (6.14) 50(4.9) p = t p = = Therefore, do ot reject 0 at the 10% alpha level ice < = t (119,.05) Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

8 10-8 Statitic for Buie & Ecoomic, 7 th editio Let Book havig more tha 100 data file; book with at mot 100 data file : 0; : 0; 0 1 9(107) 9(1681) p = 3,63,605, t = 1.75 Therefore, do ot reject 0 at the 10% alpha level ice 1.75 < 1.33 = t (18,.1) a. : P 0; : 0; 0 P P 1 P (.4) 600(.50) z pˆ o =.4636, (.4636)(1.4636) (.4636)(1.4636) p-value =.004. Therefore, reject 0 at all commo level of alpha = : P P 0; : P P 0; b (.60) 600(.64) pˆ o =.618, z (.618)(1.618) (.618)(1.618) = p-value = Therefore, reject 0 at.10, but do ot reject at the.05 level : P P 0; : P P 0; c (.4) 600(.49) pˆ o =.458, z (.458)(1.458) (.458)(1.458) = p-value =.010. Therefore, reject 0 at the.05 level, but do ot reject at the.01 level : P P 0; : P P 0; d (.5) 600(.34) z pˆ o =.99, (.99)(1.99) (.99)(1.99) p-value = Therefore, reject 0 at all commo level of alpha = -3.5 Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

9 Chapter 10: pothei Tetig: Additioal Topic 10-9 : P P 0; : P P 0; e (.39) 600(.4) pˆ o =.4064, z (.4064)(1.4064) (.4064)(1.4064) = p-value =.156. Therefore, do ot reject 0 at a commo level of alpha Let people i the Uited State were poitive about the future ecoom; people i Great Britai were poitive about the future ecoom : P P 0; : P P 0; (.60) 900(.66) pˆ o =.63, z (.63)(1.63) (.63)(1.63) = p-value = Therefore, reject 0 at all commo level of alpha Let agreed with the tatemet i coutr A; agreed with the tatemet i coutr B : P P 0; : P P 0; ˆ p o (.384) 1108(.5) z =.44, Reject 0 at all commo level of alpha (.44)(.56) (.44)(.56) = Let uer were attemptig to lear more about their optio,; uer of alterative carrier : P 0; : 0; 0 P P 1 P reject 0 if z.05 > (.5) 116(.319) pˆ o = z (.66)(.734) (.66)(.734) = Do ot reject 0 at the 5% level Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

10 10-10 Statitic for Buie & Ecoomic, 7 th editio Let people who had pledged had alread bee laid off; people who had ot pledged had alread bee laid off : P 0; : 0; 0 P P 1 P reject 0 if z.05 > pˆ o = z (.36714)(.6386) (.36714)(.6386) =.465. Reject 0 at the 5% level Let high-qualit ivetmet equit optio had le tha 30% debt; high-rik ivetmet equit optio had le tha 30% debt : P P 0; : P P 0; pˆ o = z (.614)(.386) (.614)(.386) = Reject 0 at all commo level of alpha 10.0 Let Whe aked how atified the were; Whe aked how diatified the were : P 0; : 0; 0 P P 1 P reject 0 if z.05 > pˆ o = z (.554)(.446) (.554)(.446) = Do ot reject 0 at the 5% level 10.1 Let radom ample of people i Demark; radom ample of 1,00 people i Frace : P 0; : 0; 0 P P 1 P reject 0 if z.01 < pˆ o = z (.577)(.43) (.577)(.43) = Reject 0 at the 1% level Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

11 Chapter 10: pothei Tetig: Additioal Topic a. : ; : 0 1 F = 15/51 =.451. Reject 0 at the 1% level ice.451 >.11 F (44,40,.01) b. : ; : 0 1 F = 35/15 = Reject 0 at the 5% level ice 1.88 > 1.69 F (43,44,.05) c. : ; : 0 1 F = 134/51 =.67. Reject 0 at the 1% level ice.67 >.11 F (47,40,.01) d. : ; : 0 1 F = 167/88 = Reject 0 at the 5% level ice 1.90 > 1.79 F (4,38,.05) 10.3 Let high-epertie group; low-epertie group : ; : 0 1 F = / = Reject 0 at the 1% level ice >.41F (9,9,.01) 10.4 Let active price competitio; duopol ad tacit colluio : ; : 0 1 ; reject 0 if F (3,6,.05) > 4.76 F = /16.08 = Reject 0 at the 5% level 10.5 Let auditor ot uig the cah-flow iformatio; auditor ued the cah-flow iformatio : ; : 0 1 ; F=(7.56) /(.93) =1.44. Do ot reject 0 at the 5% level ice 1.44<1.84F (35,35,.05 ) 10.6 Let Book havig more tha 100 data file; book with at mot 100 data file : ; : 0 1 ; F = (107) /(1681) = 1.57 Therefore, do ot reject 0 at the 10% level ice 1.57 < 3.18 F (9,9,.05 ) 10.7 Let with a moderator; without a moderator : ; : 0 1 ; F = (4.4) /(0.) = Do ot reject 0 at the 5% level ice 1.46 < 9.8 F (3,3,.05 ) 10.8 No. The probabilit of rejectig the ull hpothei give that it i true i 5%. Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

12 10-1 Statitic for Buie & Ecoomic, 7 th editio 10.9 Let e-moker; log-term e-moker Aumig populatio variace are equal, : 0; : 0; 0 1 ( 1) ( 1) = 33(.1) 85(1.69) = t p p = = p-value i betwee (.05,.010) =.05 ad.0. Reject 0 at level i ece of 5% Aumig populatio variace are equal, a. : 4; : 4; 0 1 reject 0 if t.05 > t =.574. Reject at the 5% level b. Let reoe for buie maager ; reoe for college ecoomic : 0; : 0; 0 1 reject 0 if t.05 < ( 1) ( 1) 69(1.3) 105(1.4) = = t p = = Reject 0 at level i ece of 5% Let bachelor degree holder ; mater degree holder : 0; : 0; 0 1 reject 0 if t.05 > ( 1) ( 1) 43(18.0) 67(18.94) = = t p = = Do ot reject 0 at level i ece of 5% Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

13 Chapter 10: pothei Tetig: Additioal Topic Let four-member group; eight-member group Preumig the populatio are ormall ditributed with equal variace, the ample mut be idepedet radom ample: : 0; : 0; 0 1 reject 0 if t (10,.01) < ( 1) ( 1) 3(4.4) 7(14.6) = = t p = = Reject 0 at level i ece of 1% Let coumptio of food group are greater i the metro; coumptio of food group are greater i the o-metro Preumig the populatio are ormall ditributed with equal variace i all the cae, the ample mut be idepedet radom ample: Per capita coumptio of fruit ad vegetable i the metro ad o-metro coutie : 0; : 0; 0 1 reject 0 = 1085, = 03, =., = 17.1 ( 1) ( 1) 1084(.) 0(17.1) = t p = = Reject 0 Per capita coumptio of ack food i the metro ad o-metro coutie = 1085, = 03, = 10., = 9.1 : 0; : 0; 0 1 reject 0 ( 1) ( 1) 1084(10.) 0(9.1) = t p = = Do ot reject 0 Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

14 10-14 Statitic for Buie & Ecoomic, 7 th editio Per capita coumptio of oft drik i the metro ad o-metro coutie = 1085, = 03, = 7.7, = 7.4 : 0; : 0; 0 1 reject 0 ( 1) ( 1) 1084(7.7) 0(7.4) = t p = = Do ot reject 0 Per capita coumptio of meat i the metro ad o-metro coutie = 1085, = 03, = 15.8, = 10.5 : 0; : 0; 0 1 reject 0 ( 1) ( 1) 1084(15.8) 0(10.5) = t p = = Reject Let Obeit rate i the metro; Obeit rate i the o-metro Aumig the populatio are ormall ditributed with equal variace, i all the cae ad idepedet radom ample: Percet of obee adult i metro ad o-metro coutie : 0; : 0; 0 1 reject 0 if t.05 < = 1089, = 051, = 3.63, = 3.58 ( 1) ( 1) 1088(3.63) 050(3.58) = t p = = Reject 0 Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

15 Chapter 10: pothei Tetig: Additioal Topic Percet of low-icome prechool obeit i metro ad o-metro coutie : 0; : 0; 0 1 reject 0 = 1015, = 1676, = 3.49, = 3.85 ( 1) ( 1) 974(3.49) 1715(3.85) = t p = = Do ot reject Let buie facult; ecoomic facult : 0; : 0; 0 1 Sample ize greater tha 100, ue the z-tet z (.89) (.67) = -.30, p-value = 1 F Z (.3) = = Therefore, reject 0 at level of alpha i ece of 1.07% Let kee patiet; hip patiet Aumig the populatio are ormall ditributed with equal variace, : 0; : 0;. Sample ize le tha 100, ue the t-tet 0 1 ( 1) ( 1) 8(.649) 53(.45) = = t p = = p-value i betwee (.05 ad.05) = ad.05. Reject 0 at a alpha of.10 or higher. : P.5; : P.5; reject 0 if z.05 < z = -1.. Do ot reject 0 (.5)(.5) /178 at the 5% level a. 0 1 Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

16 10-16 Statitic for Buie & Ecoomic, 7 th editio b. Let accoutig major; fiace major : P 0; : 0; 0 P P 1 P reject o if z.05 > z pˆ o =.478, 1 1 = (.478)(.5)( ) Therefore, do ot reject 0 at the 5% level Let firm with ubtatial earig; firm without ubtatial earig : 0; : 0; reject o if t (44,.05) < ( 1) ( 1) (.055) (.058) = 3 3 t p = = Reject 0 at a commo level of alpha = Let emploee who had ot completed high chool; emploee who had completed high chool but had ot atteded college : P P 0; : P P 0; reject o if z.01 < -.33 ˆ p o z =.11, Do ot reject 0 at the 1% level (.11)(.789)( ) = Let health iurace firm; caualt iurace firm : P P 0; : P P 0; ˆ p o z = , ( )( )( ) [1-F Z (1.4)] = [1-.895] = Reject 0 at level of alpha i ece of 10.75% = 1.35, p-value = Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

17 Chapter 10: pothei Tetig: Additioal Topic Let male cliet; female cliet : P P 0; : P P 0; z =.617, pˆ o 1 1 = , (.617)(.383)( ) p-value = 1 F Z (1.65)]=.0495 Therefore, reject 0 at level of alpha i ece of 4.95% 10.4 Let Obeit rate i the metro; Obeit rate i the o-metro Aumig the populatio are ormall ditributed with equal variace i all the cae ad idepedet radom ample: Percet of obee adult i metro ad o-metro coutie of Califoria : 0; : 0; 0 1 reject 0 if t.05 < = 37, = 1, = 3.83, = 1.69 ( 1) ( 1) 36(3.83) 0(1.69) = t p = = Do ot reject 0 Percet of low-icome prechool obeit i metro ad o-metro coutie of Califoria : 0; : 0; 0 1 reject 0 = 37, = 0, = 1.98, = 3.03 ( 1) ( 1) 36(1.98) 19(3.03) 37 0 t p = = Reject 0 = 5.7 Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

18 10-18 Statitic for Buie & Ecoomic, 7 th editio Percet of obee adult i metro ad o-metro coutie of Michiga : 0; : 0; 0 1 reject 0 if t.05 < =6, = 57, =.11, = 0.94 ( 1) ( 1) 5(.11) 56(0.94) = t p = = Do ot reject 0 Percet of low-icome prechool obeit i metro ad o-metro coutie of Michiga : 0; : 0; 0 1 reject 0 if t.05 < = 6, = 56, = 1.61, =.85 ( 1) ( 1) 5(1.61) 55(.85) = t p = = Do ot reject 0 Percet of obee adult i metro ad o-metro coutie of Mieota : 0; : 0; 0 1 reject 0 if t.05 < = 1, = 66, =1.3, = 0.71 ( 1) ( 1) 0(1.3) 65(0.71) 1 66 t p = = Reject 0 = 0.74 Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

19 Chapter 10: pothei Tetig: Additioal Topic Percet of low-icome prechool obeit i metro ad o-metro coutie of Mieota : 0; : 0; 0 1 reject 0 if t.05 < = 1, = 66, = 1.94, = 3.11 ( 1) ( 1) 0(1.94) 65(3.11) = t p = = Reject 0 Percet of obee adult i metro ad o-metro coutie of Florida : 0; : 0; 0 1 reject 0 if t.05 < = 38, = 9, = 3.38, = 3.39 ( 1) ( 1) 37(3.38) 8(3.39) = t p = = Reject 0 Percet of low-icome prechool obeit i metro ad o-metro coutie of Florida : 0; : 0; 0 1 reject 0 = 38, = 8, =.73, =.66 ( 1) ( 1) 37(.73) 7(.66) = t p = = Do ot reject 0 Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

20 10-0 Statitic for Buie & Ecoomic, 7 th editio Let tudet eligible for free luche i rural area; tudet eligible for free luche i urba areaaumig the populatio are ormall ditributed with equal variace i all the cae ad idepedet radom ample: : 0; : 0; 0 1 reject 0 = 1089, = 040, = 16.4, = ( 1) ( 1) 1088(16.4) 039(16.48) = t p = = Reject 0 Two-Sample T-Tet ad CI: PCT_FREE_LUNC, metro Two-ample T for PCT_FREE_LUNC metro N Mea StDev SE Mea Differece = mu (0) - mu (1) Etimate for differece: % upper boud for differece: T-Tet of differece = 0 (v <): T-Value = 10.9 P-Value = DF = 317 Both ue Pooled StDev = Let ued the old procedure; ued the ew procedure : 0; : 0; a. 0 1 df = 1 + = = 5; t 5,.05 = ( 1 1) 1 ( 1) (7 1)100 (7 1)150 p tcalc 1.99 p p At the.05 level of igificace, reject o ad accept the alterative that the mea output per hectare i igificatl greater with the ew procedure. b. 95% acceptace iterval: F6,6,.05.0, P(.0).95, Fcalc 1.50, becaue F calc i withi the acceptace iterval, there i ot ufficiet evidece agait the ull hpothei that the ample variace are ot igificatl differet from each other. Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

21 Chapter 10: pothei Tetig: Additioal Topic Let market 1 i weter Polad; market i outher Autria a. : P 0 P1 0; : P 1 P1 0; reject 0 if z.015 > z pˆ o =.3453, (.3453)(.6547) (.3453)(.6547) = Therefore, reject 0 at the 5% level, but do ot reject at the 3% level : P P 0; : P P 0; reject 0 if z.03 > z pˆ o =.3453, (.3453)(.6547) (.3453)(.6547) Therefore, reject 0 at the 3% level b = Let tudet eligible for free luche i rural area; tudet eligible for free luche i urba area Preumig the populatio are ormall ditributed with equal variace, the ample mut be idepedet radom ample: Eligibilit for free luche betwee rural ad urba reidet of Califoria : 0; : 0; 0 1 reject 0 = 1, = 37, =1.1, = 1.43 ( 1) ( 1) 0(1.1) 36(1.43) 1 37 t p = = Do ot reject 0 = Eligibilit for free luche betwee rural ad urba reidet of Tea : 0; : 0; 0 1 reject 0 = 176, = 77, = 1.85, = ( 1) ( 1) 175(1.85) 76(10.71) = t p = = Reject 0 Eligibilit for free luche betwee rural ad urba reidet of Florida Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

22 10- Statitic for Buie & Ecoomic, 7 th editio : 0; : 0; 0 1 reject 0 = 9, = 38, = 9.34, = 11.9 ( 1) ( 1) 8(9.34) 37(11.9) 9 38 t p = = Reject 0 = a. The bo plot of the raw data how imilar media ad iterquartile rage for both brad. owever, brad i domiated b three outlier that are kewig the brad data to the right: Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

23 Chapter 10: pothei Tetig: Additioal Topic 10-3 The decriptive tatitic how the effect of the etreme outlier o brad ale the izeable tadard deviatio of brad : ote Decriptive Statitic: aleb, aleb4 Variable N Mea Media TrMea StDev SE Mea aleb aleb Variable Miimum Maimum Q1 Q3 aleb aleb The matched pair t-tet o the origial data how a igificat differece betwee the weekl ale with brad foud to be igificatl larger tha brad 4 at the.05 level: Paired T-Tet ad CI: aleb, aleb4 Paired T for aleb - aleb4 Variable N Mea StDev SE Mea aleb aleb Differece % lower boud for mea differece: 1.5 T-Tet of mea differece = 0 (v > 0): T-Value = 1.74 P-Value = b. owever, with ol the larget outlier removed from the data of brad, the differece betwee the two brad become iigificat at the.05 level: Paired T-Tet ad CI: aleb_1, aleb4 (with outlier removed) Paired T for aleb_1 - aleb4 N Mea StDev SE Mea aleb_ aleb Differece % lower boud for mea differece: -4.6 T-Tet of mea differece = 0 (v > 0): T-Value = 1.4 P-Value = Let Sale for Ole ice cream; ale for Carl ice cream : 0; : 0; a. 0 1 Reult for: Ole.MTW Two-Sample T-Tet ad CI: Oleale, Carlale Two-ample T for Oleale v Carlale N Mea StDev SE Mea Oleale Carlale Differece = mu Oleale - mu Carlale Etimate for differece: % lower boud for differece: 475 T-Tet of differece = 0 (v >): T-Value =.5 P-Value = DF = 310 Both ue Pooled StDev = 4839 Reject 0 at the.01 level of igificace. Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

24 10-4 Statitic for Buie & Ecoomic, 7 th editio : 0; : 0; b. 0 1 Two-Sample T-Tet ad CI: Oleprice, Carlpric Two-ample T for Oleprice v Carlpric N Mea StDev SE Mea Oleprice Carlpric Differece = mu Oleprice - mu Carlpric Etimate for differece: % CI for differece: (-0.097, 0.083) T-Tet of differece = 0 (v ot =): T-Value = P-Value = 0.96 DF = 310 Both ue Pooled StDev = Do ot reject 0 at a commo level of igificace. Note that the 95% cofidece iterval cotai 0, therefore, o evidece of a differece The equatio for a acceptace iterval i how et: z / Sice the package weight are ot idepedet ( ), the variace of the ample mea i give b the followig equatio: Calculate the variace of the ample mea uig 4. Alo, ue 1 0. ad , 0.06, 1 4, ad (0.40) Thu, the tadard deviatio of the ample mea i For a 99% acceptace iterval, 0.01, o z / z The 99% acceptace iterval i , or (15.5, 16.48). The acceptace iterval ca be ued for qualit cotrol moitorig of the proce. The iterval i plotted over time ad provide limit for the ample mea. Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

25 Chapter 10: pothei Tetig: Additioal Topic Let America trade magazie advertiemet; Britih trade magazie advertiemet : P 0; : 0; 0 P P 1 P reject 0 if z z / or z z / Let 70 ad 03. The, p ˆ 56 / ad p 5 / (70)(0.074) (03)(0.56) pˆ z 1.5 (0.83)(1 0.83) (0.83)(1 0.83) Do ot reject 0 at the 5% level. Coclude that there i a ot a differece i the proportio of humorou ad i Britih veru America trade magazie Let EI o the firt da; EI o the ecod da Preumig the populatio are ormall ditributed with equal variace, the ample mut be idepedet radom ample: EI of idividual meaured o two differet da : 0; : 0; 0 1 reject 0 = 4130, = 4460, = 14.56, = 14. ( 1) ( 1) t p = = Reject 0 419(14.56) 4459(14.) = Let diet of immigrat; diet of o-immigrat Preumig the populatio are ormall ditributed with equal variace, the ample mut be idepedet radom ample: Differece i the diet of immigrat ad ative i the firt iterview : 0; : 0; 0 1 reject 0 = 885, = 3575, = 13.98, = ( 1) ( 1) 884(13.98) 3574(13.95) t p = = Reject 0 = Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

26 10-6 Statitic for Buie & Ecoomic, 7 th editio Differece i the diet of immigrat ad ative i the ecod iterview : 0; : 0; 0 1 reject 0 = 801, = 339, = 14.11, = ( 1) ( 1) 800(14.11) 338(14.33) = t p = = Reject 0 ece the immigrat have trog iteret for good diet i both the firt ad ecod iterview Let diet of phicall active people; diet of people who are ot phicall active Preumig the populatio are ormall ditributed with equal variace, the ample mut be idepedet radom ample: Differece i the diet of idividual who are phicall active ad thoe who are ot i the firt iterview : 0; : 0; 0 1 reject 0 = 77, = 183, = 14.44, = ( 1) ( 1) 76(14.44) 18(13.93) = t p = = Reject 0 Differece i the diet of idividual who are phicall active ad thoe who are ot i the ecod iterview : 0; : 0; 0 1 reject 0 = 114, = 016, = 14.77, = 14.7 ( 1) ( 1) 113(14.77) 015(14.7) = t p = = Reject 0 ece the idividual who are phicall active have trog iteret for qualit diet i both the firt ad ecod iterview Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

27 Chapter 10: pothei Tetig: Additioal Topic Let diet of igle people; diet of married people Preumig the populatio are ormall ditributed with equal variace, the ample mut be idepedet radom ample: Differece i the diet of idividual who are igle ad thoe who are married i the firt iterview : 0; : 0; 0 1 reject 0 = 1785, = 673, = 14.04, = 14.6 ( 1) ( 1) 1784(14.04) 67(14.6) = t p = = Do ot reject 0 Differece i the diet of idividual who are igle ad thoe who are married i the ecod iterview : 0; : 0; 0 1 reject 0 = 1597, = 531, = 14.8, = ( 1) ( 1) 1596(14.8) 530(14.33) = t p = = Do ot reject 0 We caot coclude about the qualit of the diet of idividual who are igle ad thoe who are married i either of the iterview Let diet of me; diet of wome Preumig the populatio are ormall ditributed with equal variace, the ample mut be idepedet radom ample: Differece i the qualit of diet betwee me ad wome i the firt iterview : 0; : 0; 0 1 reject 0 = 31, = 139, = 14.4, = ( 1) ( 1) 30(14.4) 138(13.84) = t p = = Reject 0 Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

28 10-8 Statitic for Buie & Ecoomic, 7 th editio Differece i the qualit of diet betwee me ad wome i the ecod iterview : 0; : 0; 0 1 reject 0 = 176, = 1954, = 14.49, = ( 1) ( 1) 175(14.49) 1953(14.55) = t p = = Reject 0 ece there i differece i the qualit of diet betwee me ad wome i both the iterview Let dail food cot for wome; dail food cot for me Preumig the populatio are ormall ditributed with equal variace, the ample mut be idepedet radom ample: Differece i the dail food cot betwee me ad wome i the firt iterview : 0; : 0; 0 1 reject 0 if t.05 < = 31, = 139, =.57, = 3.4 ( 1) ( 1) 30(.57) 138(3.4) = t p = = Reject 0 Differece i the dail food cot betwee me ad wome i the ecod iterview : 0; : 0; 0 1 reject 0 if t.05 < = 176, = 1954, =.49, = 3. ( 1) ( 1) 175(.49) 1953(3.) = t p = = Reject 0 ece there i differece i the dail food cot qualit of diet betwee me ad wome i both the iterview Let utritio level of people receivig food tamp; utritio level of people who are ot receivig food tamp Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

29 Chapter 10: pothei Tetig: Additioal Topic 10-9 Preumig the populatio are ormall ditributed with equal variace, the ample mut be idepedet radom ample: Differece i the qualit of diet betwee people who receive food tamp ad thoe who do t receive food tamp i the firt iterview. : 0; : 0; 0 1 reject 0 = 574, = 383, = 13.65, = 14. ( 1) ( 1) 573(13.65) 38(14.) = t p = = Do ot reject 0 Differece i the qualit of diet betwee people who receive food tamp ad thoe who do t receive food tamp i the ecod iterview. : 0; : 0; 0 1 reject 0 = 517, =3560, = 13.63, = ( 1) ( 1) 516(13.63) 3559(14.53) = t p = = Do ot reject 0 ece there i o differece i the qualit of diet betwee people who receive food tamp ad thoe who do t receive food tamp i either the firt or ecod iterview. Differece i the dail cot betwee people who receive food tamp ad thoe who do t receive food tamp i the firt iterview. : 0; : 0; 0 1 reject 0 = 574, = 383, = 3.11, = 3.05 ( 1) ( 1) 573(3.11) 38(3.05) = t p = = Do ot reject 0 Differece i the dail cot betwee people who receive food tamp ad thoe who do t receive food tamp i the ecod iterview. Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

30 10-30 Statitic for Buie & Ecoomic, 7 th editio : 0; : 0; reject 0 = 517, =3560, =.7, = ( 1) ( 1) 516(.7) 3559(.94) = t p = = Do ot reject 0 ece there i o differece i the dail cot betwee people who receive food tamp ad thoe who do t receive food tamp i either the firt or ecod iterview We wated to tet whether the immigrat populatio have a lower percetage of people that are overweight compared to the remaider of the populatio i the firt iterview. Let immigrat populatio - o-immigrat populatio : P P 0; : P P 0; 0 1 Two Proportio - 1 = Immigrat = o-immigrat Da 1 Sample X N Sample p Differece = p (1) - p () Etimate for differece: % upper boud for differece: Tet for differece = 0 (v < 0): Z = P-Value = Reject 0 at all level of alpha. We wated to tet whether the immigrat populatio have a lower percetage of people that are overweight compared to the remaider of the populatio i the ecod iterview. Let immigrat populatio - o-immigrat populatio : P P 0; : P P 0; 0 1 Two Proportio - 1 = Immigrat = o-immigrat Da Sample X N Sample p Differece = p (1) - p () Etimate for differece: % upper boud for differece: Tet for differece = 0 (v < 0): Z = P-Value = Copright 013 Pearo Educatio, Ic. publihig a Pretice all.

31 Chapter 10: pothei Tetig: Additioal Topic Reject 0 at all level of alpha. ece the percetage of overweight people i higher for immigrat tha for o-immigrat populatio i both the firt ad ecod iterview. Copright 013 Pearo Educatio, Ic. publihig a Pretice all.