1. The weight of six Golden Retrievers is 66, 61, 70, 67, 92 and 66 pounds. The weight of six Labrador Retrievers is 54, 60, 72, 78, 84 and 67.

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Frank Jordan
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1 Ecoomcs 3 Itroducto to Ecoometrcs Sprg 004 Professor Dobk Name Studet ID Frst Mdterm Exam You must aswer all the questos. The exam s closed book ad closed otes. You may use your calculators but please show your work step by step. You must show your work to receve full credt. The weght of sx Golde Retrevers s 66, 6, 70, 67, ad 66 pouds. The weght of sx Labrador Retrevers s 54, 60, 7, 78, 84 ad 67. a. What are the mea ad meda weghts for Golde Retrevers? (5 pots) Golde ( ) MedaGolde (66 67) 66.5 b. If you use the rage as a measure of dsperso, are Golde Retrevers or Labrador Retrevers weghts ths sample more dspersed? (Please compute ad compare the rages) (5 pots) RageGolde Max( Golde) M( Golde) 6 3 RageLabrador Max( Labrador) M( Labrador) Whe we use the rage as a measure of dsperso we fd that the weght of Golde Retrevers s more dspersed. c. If you use the sample varace as a measure of dsperso, are Golde Retrevers or Labrador Retrevers weghts ths sample more dspersed? The sample varace of Labrador Retrevers s 4.6 (0 pots) Golde ( X X ) [( ) ( ) ( ) ( ) ( 70.33) ( ) ] 6.06 Based o the varace the weght of Golde Retrevers s more dspersed. /6

2 d. Whch of these two measures of dsperso gves us more formato ad why? (5 pots) I thk the varace cotas more formato because t checks where all the observatos are whle the rage oly looks at the top most ad bottom most observatos.. The weght of apples s ormally dstrbuted wth mea ouces ad stadard devato 3 ouces. The weght of peaches s dstrbuted ormally wth mea 0 ouces ad stadard devato ouce a. What s the probablty that a radomly selected apple wll wegh betwee 8 ad ouces? (It may help to clude a pcture of the dstrbuto) (0 pots) 8 Pr(8 Apple ) Pr Z 3 3 ( ) ( ) ( Z ) Pr Z.66 Pr.66 Pr( Z ) b. What s the probablty that f you radomly select a peach ad a apple they both wegh less tha 8 ouces? (0 pots) Pr( Apple 8 Peach 8) Pr( Apple 8)*Pr( Peach 8) 8 80 Pr Z *Pr Z 3 Pr( Z )*Pr( Z ) 0.587* ( ) ( ) /6

3 3. You have a far 3 sded de wth umbers, ad 3 o ts faces. You roll t twce. The radom varable of terest X s the sum of the two rolls of the de. a. Please workout ad draw the probablty dstrbuto of the radom varable X. (0 pots) Pr( X ) Pr( roll )*Pr( roll ) * 3 3 Pr( X 3) Pr( roll )*Pr( roll ) Pr( roll )*Pr( roll ) 3 Pr( X 4) Pr( roll )* Pr( roll 3) Pr( roll 3)* Pr( roll ) Pr( roll )* Pr( roll ) Pr( X 5) Pr( X 6) b. What s the probablty that the radom varable X takes o a value of 4 or more? (0 pots) Pr( X 4) Pr( X 4X 5X 6) Pr( X 4) Pr( X 5) Pr( X 6) /6

4 4. We are terested the relatoshp betwee the umber of hours per week a perso studes ad how they perform o the fal exam. The followg relatoshp holds the populato Exam B0 B hrs _ study u. We pck a radom sample of studets ad get the umbers below. X=hrs_study Y=Exam a. Compute B 0 ad B (0 pots) B ( x x)( y y) ( x x) Buch of algebra B 4.35 B o y B x * b. Please plot the data above ad lay the regresso le you just computed over t. (5 pots) Exam Score Hours Studed 4/6

5 c. If assumptos -4 hold what would we expect someoe who does t study to get o the exam? (ht: what does the equato computed above predct whe hrs _ study = 0?) (0 pots) We would expect someoe who does ot study to get a o the exam because that s the predcted score whe hours of studyg s equal to 0. It s ok to pot out ths t ot realstc because t s pretty far out of sample. d. If assumptos -4 hold how much would we expect a studets exam score to mprove f they study oe addtoal hour per week? (5 pots) We would expect a studet that creased ther studyg by hour per week to crease ther exam score by 4.35 pots. Ths s the slope of our regresso le. e. Oe of the four assumpto we eed for B to be a ubased estmate of B s that Eu ( x) 0. Is ths assumpto reasoable ths settg? Why or why ot? (5 pots) I thk ths assumpto s urealstc. u cotas all the uobservable determats of exam performace such as class attedace ad secto attedace. Both class ad secto attedace are lkely to be correlated wth the umber of hours a studet studes. Ths meas that the assumpto 3 fals because for hgh levels of x (Attedace) Eu ( x) 0ad for low values of x Eu ( x) 0 5/6

6 Extra Credt: I the followg regresso (f assumptos -4 hold) how much would we expect a persos wage to crease f they retur to school ad get oe addtoal year of educato? (4 pots) log( wage).64.08educ If a perso returs to school I would expect ther wage to crease by 8%. Useful Formulas Sample Varace = ( X X ) B ( x x)( y y) ( x x) B o y B x 6/6

Midterm Exam 1, section 2 (Solution) Thursday, February hour, 15 minutes

Midterm Exam 1, section 2 (Solution) Thursday, February hour, 15 minutes coometrcs, CON Sa Fracsco State Uverst Mchael Bar Sprg 5 Mdterm xam, secto Soluto Thursda, Februar 6 hour, 5 mutes Name: Istructos. Ths s closed book, closed otes exam.. No calculators of a kd are allowed..