Eco 371 Exam #1 Multiple Choice (5 poits each): For each of the followig, select the sigle most appropriate optio to complete the statemet 1) The probability of a outcome a) is the umber of times that the outcome occurs i the log ru b) equals M N, where M is the umber of occurreces ad N is the populatio size c) is the proportio of times that the outcome occurs i the log ru d) equals the sample mea divided by the sample stadard deviatio ) The cumulative probability distributio shows the probability a) that a radom variable is less tha or equal to a particular value b) of two or more evets occurrig at oce c) of all possible evets occurrig d) that a radom variable takes o a particular value give that aother evet has happeed 3) Two radom variables X ad are idepedetly distributed if all of the followig coditios hold, with the exceptio of a) Pr( = y X = x) = Pr( = y) b) kowig the value of oe of the variables provides o iformatio about the other c) if the coditioal distributio of give X equals the margial distributio of d) E ( ) = EE [ ( X)] 4) Assume that is ormally distributed N( μ, σ ) To fid Pr( c1 c), where c1 < c ad ci μ di =, you eed to calculate 1 σ Pr( d Z d ) = a) Φ( d) Φ( d1) b) Φ(196) Φ( 196) c) Φ( d) (1 Φ( d1)) 1 ( Φ( d ) Φ( d )) d) 1 5) A estimator is a) a estimate b) a formula that gives a efficiet guess of the true populatio value c) a radom variable d) a oradom umber 1
6) A estimate is a) efficiet if it has the smallest variace possible b) a oradom umber c) ubiased if its expected value equals the populatio value d) aother word for estimator 7) With iid samplig each of the followig is true except a) E( ) = μ b) var( ) = σ / c) E( ) < E() d) is a radom variable 8) Amog all ubiased estimators that are weighted averages of,, 1, is a) the oly cosistet estimator of μ b) the most efficiet estimator of μ c) a umber which, by defiitio, caot have a variace d) the most ubiased estimator of μ Problems: Provide the requested iformatio for each of the followig questios Be sure to show your work 9) (0 poits) Followig Alfred Nobel s will, there are five Nobel Prizes awarded each year These are for outstadig achievemets i Chemistry, Physics, Physiology or Medicie, Literature, ad Peace I 1968, the Bak of Swede added a prize i Ecoomic Scieces i memory of Alfred Nobel ou thik of the data as describig a populatio, rather tha a sample from which you wat to ifer behavior of a larger populatio The accompayig table lists the joit probability distributio betwee recipiets i ecoomics ad the other five prizes, ad the citizeship of the recipiets, based o the 1969-001 period
Joit Distributio of Nobel Prize Wiers i Ecoomics ad No-Ecoomics Disciplies, ad Citizeship, 1969-001 US Citize No-US Citize Total ( = 0 ) ( = 1) Ecoomics Nobel 0118 0049 0167 Prize ( X = 0 ) Physics, Chemistry, 0345 0488 0833 Medicie, Literature, ad Peace Nobel Prize ( X = 1) Total 0463 0537 100 a) Compute E ( ) ad iterpret the resultig umber b) Calculate ad iterpret E ( X= 1) ad E ( X= 0) c) A radomly selected Nobel Prize wier reports that he is a o-us citize What is the probability that this geius has wo the Ecoomics Nobel Prize? A Nobel Prize i the other five disciplies? 10) (15 poits) Fid the followig probabilities: a) is distributed χ 4 Fid Pr( > 949) b) is distributed t Fid Pr( > 05) c) is distributed F4, Fid Pr( < 33) 3
11) (15 poits) The accompayig table gives the outcomes ad probability distributio of the umber of times a studet checks her e-mail daily: Probability of Checkig E-Mail Outcome (umber of e- mail checks) Probability distributio 0 1 3 4 5 6 005 015 030 05 015 008 00 a) Calculate the cdf for the above table b) What is the probability of her checkig her e-mail betwee 1 ad 3 times a day? c) Of checkig it more tha 3 times a day? 1) (15 poits) Adult males are taller, o average, tha adult females Visitig two recet America outh Soccer Orgaizatio (ASO) uder 1 year old (U1) soccer matches o a Saturday, you do ot observe a obvious differece i the height of boys ad girls of that age ou suggest to your little sister that she collect data o height ad geder of childre i 4th to 6th grade as part of her sciece project The accompayig table shows her fidigs Height of oug ad, Grades 4-6, i iches s 578 39 55 584 4 57 s a) Let your ull hypothesis be that there is o differece i the height of females ad males at this age level Specify the alterative hypothesis 4
b) Fid the differece i height ad the stadard error of the differece c) Calculate the t-statistic for comparig the two meas Is the differece statistically sigificat at the 1% level? 13) (15 poits) IQs of idividuals are ormally distributed with a mea of 100 ad a stadard deviatio of 16 If you sampled studets at your college ad assumed, as the ull hypothesis, that they had the same IQ as the populatio, the i a radom sample of size a) = 5, fid Pr( < 105) b) = 100, fid Pr( > 97) c) = 144, fid Pr(101 < < 103) 5