MATHEMATICS LW Quantitative Methods II Martin Huard Friday April 26, 2013 TEST # 4 SOLUTIONS

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ATHATICS 360-55-L Quatitative ethod II arti Huard Friday April 6, 013 TST # 4 SOLUTIONS Name: Awer all quetio ad how all your work.

1 ATHATICS L Quatitative ethod II arti Huard Friday April 6, 013 TST # 4 SOLUTIONS Name: Awer all quetio ad how all your work. Quetio 1 (10 poit) To oberve the effect drikig a Red Bull ha o cocetratio, a pychologit gave a tet that meaure cocetratio to a radom group of 5 adult (with reult o a cale of 1 to 0, where a higher core idicate a higher level of cocetratio) before ad after drikig a Red Bull. Here are the reult. Before After d = A - B 3-6 Ca you coclude, at the 5% level of igificace, that drikig a Red Bull improve cocetratio? Ue the p-value approach. Aume that cocetratio core are ormally ditributed. Step 1 Aumptio: XB NB, B XA NA, A = 0.05 Step H : 0 0 d H A: d 0 Right-tailed tet d d. 0 t d p value Step 4 p-value > > 0.05 d d thu t Fail to reject H 0. There i ot ufficiet evidece at the 5% level of igificace to coclude that drikig Red Bull improve cocetratio. d t 4

2 Tet 4 - Solutio Quetio (10 poit) I order to look ito the tudy habit of CGP tudet, a ociologit took a radom ample of 15 tudet i their firt emeter ad aother radom ample of 16 tudet i their lat emeter, to oberve the differece i the umber of hour pet tudyig durig a week. I the ample with firt emeter tudet, the mea umber of hour tudied wa 7.3 with a tadard deviatio of 3.7 ad for the ample with the lat emeter tudet, the mea wa 9.5 hour with a tadard deviatio of 4.1 hour. Cotruct a 95% cofidece iterval for the differece i the mea umber of hour tudied i a week by firt ad lat emeter tudet. Aume that the umber of hour tudied durig a week i ormally ditributed. Step 1 Aumptio: The ample are idepedet 1 X X N N,, thu t Level of cofidece: , 0.05 Step Poit etimate: xl xf hour a) t t, 9, df Step 4 b) p x x 1 1 p 1 L 1 L F 1 F L F t , p df c) x x x x The 95% cofidece iterval for the differece i the mea umber of hour tudied i a week by firt ad lat emeter tudet i hour to 5.08 hour. t 9 iter 013 arti Huard

3 Tet 4 - Solutio Quetio 3 (10 poit) I a urvey of 900 me ad 600 wome, 45 me ad 50 wome aid they will watch at leat oe game of the hockey playoff. At the % level of igificace, ca you coclude that the proportio of me who watch at leat oe game of the playoff i differet tha the proportio of wome? Ue the claical approach. Step 1 Aumptio: pˆ 45 5 qˆ ˆ 50 5 ˆ p q Sample are idepedet. Thu pˆ ˆ p N 0, pq 1 = 0.0 Step H : 0 p p 0 Step 4 H A : p p 0 Two-tailed tet z z pˆ p pˆ ˆ p z pq ˆ ˆ p p a) z i ot i the critical regio b) Fail to reject H o. There i iufficiet evidece at the % level of igificace to coclude that the proportio of me who watch at leat oe game of the otreal Caadia agait the Boto Brui durig the playoff i differet tha the proportio of wome. iter 013 arti Huard 3

4 Tet 4 - Solutio Quetio 4 (10 poit) A radom ample of 100 CGP tudet wa elected where each wa aked for hi mother togue ad whether they are plaig to go to a Frech or a glih uiverity. Ca you coclude, at the 5% level of igificace, the uiverity a CGP tudet goe to i ot idepedet of hi mother togue? Ue the claical approach. Laguage of Uiverity other Togue Frech glih Frech (30) (0) glih (18) (1) Other (1) (8) Step 1 Step Aumptio: The clae are all icluive ad mutually excluive O i, j 5 Thu = 0.05 H o : The uiverity a CGP tudet goe to i idepedet of hi mother togue. H A : The uiverity a CGP tudet goe to i ot idepedet of hi mother togue. Step 4 a) Right-tailed tet df,, O i ot i the critical regio b) Fail to reject H o. There i iufficiet evidece at the 5% level of igificace to coclude that the uiverity a CGP tudet goe to i depedet of hi mother togue. iter 013 arti Huard 4

5 Tet 4 - Solutio Quetio 5 (10 poit) The ower of a pychotherapy cliic i tudyig the ometime large pread i waitig time for patiet to obtai a appoitmet for coultatio. I a radom ample of 5 patiet, the tadard deviatio for the waitig time wa 3.4 day. Aumig that the waitig time are ormally ditributed, fid a 95% cofidece iterval for the variace ad for the tadard deviatio of the waitig time for patiet to obtai a appoitmet for coultatio. 1 Step 1 Aumptio: X N, thu 4 Level of cofidece: or 0.05 Step Poit timate: 3.4 day a),1 4, df, 4, df b) day df, df, The 95% cofidece iterval for the variace of waitig time i 7.05 day to.37 day, ad the tadard deviatio i.65 day to 4.73 day. iter 013 arti Huard 5

6 Tet 4 - Solutio Formula d d t d t 1 1 X1 X N 1, 1 x x 1 1 t t 1 p 1 pˆ1 pˆ N p1 p, p q p q 1 pˆ1 pˆ N 0, pq 1 pˆ p p r1 r O O R 1C 1 row total colum total 1 1 df, df,1 grad total iter 013 arti Huard 6

M227 Chapter 9 Section 1 Testing Two Parameters: Means, Variances, Proportions

M227 Chapter 9 Section 1 Testing Two Parameters: Means, Variances, Proportions M7 Chapter 9 Sectio 1 OBJECTIVES Tet two mea with idepedet ample whe populatio variace are kow. Tet two variace with idepedet ample. Tet two mea with idepedet ample whe populatio variace are equal Tet