Stat13 Homework 7. Suggested Solutions

Transcription

1 Sa3 Homework 7 hp:// Suggeed Soluion Queion 7.50 Le denoe infeced and denoe noninfeced. H 0 : Malaria doe no affec red cell coun (µ µ ) H A : Malaria reduce red cell coun (µ <µ ) We noe ha y > y, o he daa do no deviae from H 0 in he direcion pecified by H A. Thu, P>0.50 H 0 i no rejeced. There i no evidence ha malaria reduce red cell coun in hi populaion. Same a par (a). Noe: If H A i revered (µ >µ ), hen H 0 would be rejeced a α0.0. Thu, hi exercie illurae he imporance of he direcionaliy check. Queion 7.5 Le denoe experimen (o be hypnoized) and denoe conrol SE ( y ) y Wih df n + n 4, Table 4 give. 64 and H 0 : Mean venilaion i he ame in he o be hypnoized condiion han in he conrol condiion (µ µ ). H A : Mean venilaion i differen in he o be hypnoized condiion han in he conrol condiion (µ µ ) H 0 i rejeced. There i ufficien evidence (0.0<P<0.0) o conclude ha mean venilaion i higher in he o be hypnoized condiion han in he conrol condiion..005

2 H 0 : Mean venilaion i he ame in he o be hypnoized condiion han in he conrol condiion (µ µ ). H A : Mean venilaion i higher in he o be hypnoized condiion han in he conrol condiion (µ >µ ) H 0 i rejeced. There i ufficien evidence (0.005<P<0.0) o conclude ha mean venilaion i higher in he o be hypnoized condiion han in he conrol condiion. Par (c): The nondirecional alernaive (par (a)) i more appropriae. According o he narraive, he reearcher formulaed he direcional alernaive in par (b) afer hey had een he daa. Thu, i would no be legiimae for hem o ue a direcional alernaive. Queion 7.5 Le denoe experimen (o be hypnoized) and denoe conrol (α0.). H 0 : Exra nirogen doe no enhance plan growh (µ µ ). H A : Exra nirogen doe enhance plan growh (µ <µ ) SE ( y ) y Wih df n + n 8, Table 4 give. 397 and H 0 i rejeced. There i ome evidence (0.05<P<0.0) o conclude ha exra nirogen enhance plan growh under hee condiion..05 Queion 7.55 The bound of p-value i: 0.03<p-value<0.05. Thu, we would rejec H 0 and conclude ha ancy doe, indeed, inhibi growh. Queion 7.57 The proponen are confued. They are peaking a if i i known ha µ µ 4lb/acre, wherea he field rial indicae only ha y y 4 lb/acre. Tha aiician daa analyi indicae ha he rial give only weak informaion abou µ µ ; in fac, he reul do no even how wheher µ µ i poiive, le alone ha i i equal o 4lb/acre. Queion 7.59 Le denoe male and denoe female.

3 CI SE ( y y ) ( ) ± (.977)( 0.857) (.6,. 6 ), uing df40 We can be 95% confiden ha he mean difference doe no exceed.6 bea per minue, which i mall and unimporan (in comparion wih, for example, ordinary flucuaion in hear rae from one minue o he nex.) Queion 7.65 Table 5 give n39. Table 5 give n30. µ µ σ Queion 7.80 Le denoe experimenal (o be hypnoized) and denoe conrol. H 0 : Venilaion i no differenly affeced by he o be hypnoized and he conrol condiion. H A : Venilaion i differenly affeced by he o be hypnoized and he conrol condiion. K 53, K, U S 53 Wih n8 and n 8, Table 6 give 0.0<P<0.05. H 0 i rejeced. There i ufficien evidence (0.0<P<0.05) o conclude ha venilaion rae end o be higher under he o be hypnoized condiion han under he conrol condiion. Queion 7.8 U S 9. Wih nn 3, U S 9 i under he 0.0 heading and i he large enry lied. Thu, 0.05<P<0.0. U S 6. Wih nn 4, U S 6 i under he 0.05 heading and i he large enry lied. Thu, 0.0<P<0.05. U S 5. Wih nn 5, U S 5 i under he 0.0 heading and i he large enry lied. Thu, 0.00<P<0.0.

4 Queion 7.8 H 0 : There i no ex difference in preening behavior. H A : There i a ex difference in preening behavior. From nn 5, he large criical value i 89, which i under he 0.00 heading for a nondirecional alernaive. I follow P<0.00, o H 0 i rejeced. There i ufficien evidence (P<0.00) o conclude ha female end o preen longer han male. H 0 : There i no ex difference in preening behavior. (µ µ ) H A : There i a ex difference in preening behavior. (µ µ ) Wih df n + n 8, Table 4 give. 467 and , o ha <P<0.0. Formula (7.) yield df5. and he conervaive approach of df min{n-,n -} give df4. For eiher of hee df value we ge 0.0<P<0.04. In any cae, H 0 i no rejeced, ince P>0.0. There i ufficien evidence o conclude ha here i a ex difference in preening behavior. Par (c): Boh e require independen, random ample. The condiion required for he -e bu no for he Wilcoxon-Mann-Whiney e i ha he populaion diribuion are normal. The frequency diribuion for he female i highly kewed, due o he wo large obervaion of 0.7 and.7. Thi ca doub on he normaliy condiion. Par (d): K K ( ) ( ) ( ) 5 where denoe male and denoe female. Queion 7.83 Le denoe ingly houed and le denoe group-houed. H 0 : There i no difference in benzo(a)pyrene concenraion beween ingly houed and group-houed mice. H A : Benzo(a)pyrene concenraion end o be higher in group-houed mice han in ingly houed mice. K 0, K 5, U S 5 and he hif in he daa i in he direcion prediced by H A. Wih nn 5, U S 5 i under he heading for a direcional alernaive and i he large enry lied. Thu,

5 0.00<P<0.005 and H 0 i rejeced. There i ufficien evidence (0.00<P<0.005) o conclude ha benzo(a) pyrene concenraion end o be higher in group-houed mice han in ingly houed mice. A direcional alernaive i valid in hi cae becaue he reearcher were inveigaing he hypohei ha licking or biing oher mice lend o increae benzo(a)- pyrene concenraion. If acce o oher mice affec benzo(a)pyrene concenraion, he effec would be o increae he concenraion; a decreae i no plauible. Queion 7.84 Le denoe jogger and le denoe fine program enran. H 0 : There i no difference in reing blood concenraion of HBE beween jogger fine program enran. H A : There i difference in reing blood concenraion of HBE beween jogger fine program enran. K 93.5, K 7.5, U S 93.5 Wih n5 and n, 08 i under he 0.0 heading for a nondirecional alernaive and i he malle enry lied. Thu, P>0.0 and H 0 i no rejeced. There i inufficien evidence (P>0.0) o conclude ha here i a difference in reing blood concenraion of HBE beween jogger fine program enran. Queion 7.89 H 0 : Mechanical milking doe no produce differen cell coun han manual milking (µ µ ). H A : Mechanical milking produce higher cell coun han manual milking (µ >µ ) Wih df8, Table 4 give.4 and Formula (7.) yield df9. 9; wih df9, Table 4 give.6and Uing eiher df value, P<0.05 and H0 i rejeced. There i ufficien evidence o conclude ha mechanical milking produce higher cell coun han manual milking. (The daa uppor he inveigaor upicion) H 0 : Mechanical milking doe no produce differen cell coun han manual Milking. H A : Mechanical milking produce higher cell coun han manual milking. U S 69. The hif in he daa i in he direcion prediced by H A. Wih nn 0, he enry under 0.0 for a direcional alernaive i 68 and he enry under 0.05 for a.0.0

6 direcional alernaive i 73. Thu, we do no rejec H 0. There i inufficien evidence (0.05<P<0.0) o conclude ha mechanical milking produce higher cell coun han manual milking (The daa do no uppor he inveigaor upicion). [Noe ha hi conradic he concluion from par (a)]. Par (c): Boh e require independen, random ample. The condiion required for he -e bu no for he Wilcoxon-Mann-Whiney e i ha he populaion diribuion are normal. The frequency diribuion for he mechanical group i highly kewed, wih ome obervaion (996 and 345) ha are much greaer han he oher. Thi ca doub on he normaliy condiion. Par (d): K K where denoe mechanical and denoe manual. Queion 7.93 Le denoe Vermilion River and le denoe Black River. H 0 : The populaion from which he wo ample were drawn have he ame diribuion of ree pecie per plo. H A : Biodiveriy i greaer along he Vermilion River han along he Black River. K.5, K 06.5, U S 80 The daa deviae from H 0 i he direcion pecified by H A. Wih nn 3 and a direcional alernaive, he 0.0 enry in Table 6 i 79 and he 0.05 enry i 84. Thu, he p-value i beween 0.05 and 0.0, o we rejec H 0. There i ufficien evidence (0.05<P<0.0) o conclude ha biodiveriy i greaer along he Vermilion River han along he Black River. Queion 7.95 H 0 : Ovarian ph i no relaed o progeerone repone (µ µ ). H A : Overian ph i relaed o progeerone repone (µ µ ). Wih df, Table give SE ( y ) y Thu, P<0.00, o we rejec H0. There i ufficien evidence (P<0.00) o conclude ha ovarian ph i lower among reponder o propeerone han among nonreponder.

7 Queion 7.99 Le denoe low chromium and le denoe normal. H 0 : Low chromium die doe no affec GITH (µ µ ). H A : Low chromium die doe affec GITH (µ µ ). y y Formula (7.) give df.9; SE ( y ). 970 y , o P>0.40. Uing a compuer, we ge ( ) P0.48. Thu, we do no rejec H0. There i inufficien evidence (P0.48) o conclude ha low chromium die affec GITH in ra. Queion 7.0 CI ( ) ± (.074)(.970) ( 5.5,. 7 ), uing df All value in he confidence inerval are maller in magniude han 8000 cpm/gm; hu he daa uppor he concluion ha he difference i unimporan. Par (c): The confidence inerval indicae ha he difference could be larger in magniude han 4000 cpm/gm or maller; hu he daa do no indicae wheher he difference i unimporan. Queion 7.04 Fale. The confidence inerval include zero, o we are no confiden ha µ and µ are differen. True. Thi i wha a confiden inerval ell u. Par (c): Fale. We know ha y y Par (d): Fale. The confidence inerval i ued o make an inference abou he difference beween µ and µ ; i doe no ell u abou individual daa poin (uch a he lengh of hopializaion for a niric oxide infan).