Exam 2 Istructios Remove this sheet of istructios from your exam. You may use the back of this sheet for scratch work. This is a closed book, closed otes exam. You are ot allowed to use ay materials other tha the exam istructio sheet, the provided formula sheet, ad a calculator. The exam cosists of 25 questios. Make sure that you have a complete exam. Studets are ot allowed to pass calculators back ad forth. There are multiple versios of the exam. It will ot help to copy from the perso ext to you. Each correct aswer is worth 4 poits. If you omit the aswer to a questio you will receive o poits (zero poits) for that questio. If you icorrectly aswer a questio you will receive o poits (zero poits) for that questio. There will be o poits deducted for a icorrect aswer. Guessig the aswer to a questio IS permitted o this exam.
! ( 1) K 2 1! m m!( m)! rel.freq. freq. SS(x) Σx 2 (Σx)2 SS(y) Σy 2 (Σy)2 SS(xy) Σxy (Σx)(Σy) Σ(x x ) 2 Σ(y y ) 2 Σ(x x )(y y ) x Σx r SS(xy) SS(x) SS(y) µ Σx N s σ s 2 σ 2 1 2 +1 ( ) Σ(x x )2 1 Σ(x µ)2 N Σ(x x)2 1 Σ(x µ)2 N skew 3(x x ) s IQR Q 3 Q 1 z x µ σ Σx 2 (Σx)2 1 Σx 2 (Σx)2 1 r Σxy (Σx)(Σy) Σx 2 (Σx)2 Σy 2 (Σy)2 1 r Σ x x y y 1 s x s y 1 1 r 1 s x s Σ(x x )(y y ) y y b 0 + b 1 x b 1 SS(xy) SS(x) b 1 Σxy (Σx)(Σy) b 1 r s y Σx 2 (Σx)2 s x b 0 y b 1 x residual y ˆ y SSE Σ(y y ˆ ) 2
P(A) r m ˆ p x ˆ P (A) k P(otA) 1 P(A) P(A B) P(A) + P(B) P(A B) e 2.718281828 P(X) e λ λ x,x 0,1,2,... x! µ λ P(A B) P(A) + P(B) σ λ P(A B) P(A) P(B A) P(A B) P(B) P(A B) P(A B) P(A) P(B) P(A B) P(B A) P(A B) P(B) P(A B) P(A) P(A) P(A B) ad P(B) P(B A) E(X) µ x Σx p(x) E(X) µ x p σ x 2 Σ(x µ x ) 2 p(x) σ x Σ(x µ x ) 2 p(x) P(X) p x (1 p) x,x 0,1,2,..., x µ p σ p(1 p) p 0.1, 25, p 10, λ p p > 5, (1-p) > 5 x truevalue + bias + radomerror x µ + bias µ x µ σ x σ x SE(X ) σ x E(X ) µ x z x µ σ z x µ x µ σ σ x x ±1.96 σ x ±1.96 s
x ± Crit.Val. SE(X ) x ± z * B z s s ˆ p > 5,(1 p ˆ ) > 5 SE( ˆ p ) p ˆ ± z SE( p ˆ ) ˆ p ± z x ± z p ˆ (1 p ˆ ) p ˆ (1 p ˆ ) x 1 x For 90% C.L. z1.645 For 95% C.L. z1.960 For 99% C.L. z2.578 α 2 ( 1 C.L. ) 2 t x µ s (x y ) ± z s 2 x + s y m (x y ) ± t +m 2 s p 1 + 1 m d.f. + m 2 s p d ± t 1 d ± z d Σd ( 1) s 2 2 x + (m 1) s y + m 2 s d s d 2 p ˆ (1 p ˆ ) B z s x ± t 1 * s d ˆ p 1 x Σd 2 (Σd)2 1 Σ(d d )2 1 d.f. - 1 C.L. 1 - α α 1 C.L. ˆ p 2 y m ˆ p 1 > 5 (1 ˆ p 1 ) > 5 mˆ p 2 > 5 m(1 ˆ p 2 ) > 5
( p ˆ 1 p ˆ 2 ) ± z z ˆ p p p(1 p) T x µ 0 s Z x µ 0 σ T d µ d s d p ˆ 1 (1 p ˆ 1 ) + p ˆ 2(1 p ˆ 2 ) m Z ( p ˆ 1 p ˆ 2 ) (p 1 p 2 ) p ˆ (1 p ˆ ) 1 + 1 m p ˆ x + y + m α P(TypeI) β P(TypeII) E i p i d.f. k-1 χ 2 * E (O E)2 E rowtotal columtotal T x y (µ µ ) x y s p 1 + 1 m Z T (x y ) (µ x µ y ) s x 2 2 + s y m E ij row i colum j d.f. (r-1)(c-1) χ 2 * (O E 0.5)2 E
1. The formula E(X) p ca be used to fid the expected value of a. ay umeric radom variable b. oly Poisso radom variables c. oly ormal radom variables d. oly biomial radom variables e. oe of the above 2. For a specific sample size, the width of a 95% cofidece iterval o µ a. would be larger tha the width of a 90% cofidece iterval o µ. b. would be smaller tha the width of a 90% cofidece iterval o µ. c. would be the same as the width of a 90% cofidece iterval o µ. d. caot be compared to the width of a 90% cofidece iterval o µ. e. oe of the above 3. A radom sample of 400 WVU studets was selected, i which 150 studets stated that they had used a illegal drug. A 95 % cofidece iterval o biomial parameter p goes from 33.5% to 41.5%. Which of the followig statemets provides the appropriate iterpretatio of this 95 % cofidece iterval? a. 95% of all WVU studets use a illegal drug betwee 33.5% ad 41.5% of the time. b. There is a 95% probability that a radomly selected WVU studet has used a illegal drug. c. We are 95% cofidet that betwee 33.5% ad 41.5% of all WVU studets have used a illegal drug. d. We are 95% cofidet that betwee 33.5% ad 41.5% of the sample of 400 WVU studets have used a illegal drug. e. oe of the above 4. The stadard ormal distributio is a ormal distributio whose a. mea is µ1 ad stadard deviatio σ0 b. mea is µ0 ad stadard deviatio σ1 c. mea µ ca have ay real value ad stadard deviatio σ1 d. mea µ ca be determied by usig a z-score e. oe of the above 5. A radar gu is used to measure the speed of 74 radomly selected automobiles o Iterstate 79, ad the data is used to costruct a 95% cofidece iterval o the mea speed of all automobiles o I-79. The 95 % cofidece iterval goes from 64.4 mph to 71.6 mph. Which of the followig statemets provides the appropriate iterpretatio of this 95 % cofidece iterval? a. 95% of all automobiles o I-79 travel betwee 64.4 mph ad 71.6mph.
b. There is a 95% probability that the mea speed of all automobiles o I-79 is betwee 64.4 mph ad 71.6 mph. c. We are 95% cofidet that the mea speed of all automobiles o I-79 is betwee 64.4 mph ad 71.6 mph. d. There is a 5% probability that the mea speed of all automobiles o I-79 is betwee 64.4 mph ad 71.6 mph. e. oe of the above 6. Scores o the math sectio of a college etrace exam are ormally distributed with mea µ 22.4 ad stadard deviatio σ3.1. Fid the probability that a radomly selected test-taker will score 25 or higher o the math sectio of this exam. a. 0.7995 b. 0.2005 c. 0.8387 d. 0.1613 e. oe of the above 7. Every ormal distributio a. is symmetric about its mea µ0 b. is symmetric about its mea µ, but the mea is ot ecessarily 0 c. is asymmetric d. parts b) ad c) oly e. oe of the above 8. O a multiple-choice exam, there are 5 possible aswers to each of 20 questios. Each questio has oly oe correct aswer. A studet, J, has ot studied ad must guess the aswer to each questio (you may assume that the guesses are idepedet of each other). The mea umber of correct guesses that J ca expect to obtai is a. 5 b. 10 c. 4 d. 2 e. oe of the above 9. A radom sample of 400 WVU Stat211 studets was selected, i which 72 studets stated that they did ot atted their statistics lab sessio last week. A 99% cofidece iterval o p, the probability that a radomly selected WVU Stat211 studet did ot atted his/her statistics lab sessio last week a. has lower limit 0.142 ad upper limit 0.218 b. has lower limit 0.148 ad upper limit 0.211 c. has lower limit 0.130 ad upper limit 0.230 d. caot be computed usig the iformatio provided
e. is oe of the above Statistics 211 Practice Exam 2 10. Twety-three percet of college freshme do ot retur to college for their sophomore year of study. A radom sample of 12 college freshme is obtaied. The probability that exactly four of the 12 freshme will ot retur for their sophomore year is a. 0.1712 b. 0.0010 c. 0.8424 d. 0.1936 e. oe of the above 11. A radom sample cosistig of 64 observatios is collected from a populatio with mea 75 ad stadard deviatio 32. The probability that the sample mea will have value that is less tha 83 is a. ot computable give the iformatio provided b. 0.5987 c. 0.0228 d. 0.9772 e. oe of the above 12. Before we use the Poisso distributio to approximate a biomial probability, we must a. make sure that the origial experimet is a biomial experimet b. check that the (three) coditios for usig the Poisso approximatio are satisfied c. set λp d. all of the above e. parts b) ad c) oly 13. Vedco Compay ows a soda pop vedig machie i the lobby of their office buildig. For a radom sample of 14 days durig the year 2004, data was collected o the umber of cas of soda pop sold each day. The sample mea was 65.2 cas with a sample deviatio of 8.1 cas. Costruct a 95% cofidece iterval o the mea umber of ca sold per day durig 2004. a. The 95 % cofidece iterval goes from 60.96 to 69.44 cas per day. b. The 95 % cofidece iterval goes from 60.52 to 69.88 cas per day. c. The 95 % cofidece iterval goes from 61.64 to 68.76 cas per day. d. The 95 % cofidece iterval caot be calculated because the sample size is less tha 30 observatios. e. The 95 % cofidece iterval goes from 57.10 to 73.30 cas per day.
14. Assume that the amout of time PRT riders sped waitig for a PRT car is ormally distributed with a mea µ 14.8 miutes ad stadard deviatio σ2.9 miutes. Fid the probability that a radomly selected PRT rider must wait less tha 18 miutes for the ext PRT car. a. 1.1034 b. 0.1100 c. 0.8643 d. 0.1357 e. oe of the above 15. A idividual measuremet, i.e., a data value, cosists of which three compoets: a. the sample, the observatioal uit, ad the researcher b. the true value, the bias, ad chace (or radom) error c. the populatio, the sample, ad the sample mea d. the populatio mea, the sample mea, ad the sample stadard deviatio e. oe of the above 16. A radom sample of 10 observatios is selected from a ormal distributio with populatio mea equal to 75 ad a populatio stadard deviatio equal to 20. The mea of x-bar s distributio (i.e., the samplig distributio of the sample mea) a. caot be determied from the iformatio provided b. will be equal to 75 c. will be equal to 20 d. will be equal to 7.5 e. oe of the above 17. Dr. Digme, a archaeologist, estimates that, o the average, she recovers oe sigificat historical artifact per fifty cubic yards of dirt that she excavates. Durig the summer of 2007 Dr. Digme plas to excavate 100 cubic yards of dirt. The probability that Dr. Digme will recover at least 3 sigificat historical artifacts is a. 0.677 b. 0.323 c. 0.080 d. 0.019 e. oe of the above 18. Hot Head Hat Compay specializes i custom pritig o hats. Hot Head Hat Compay averages two custom orders per week. The probability that this compay receives exactly 3 custom hat orders ext week is a. 0.180 b. 0.820
c. 0.857 d. 0.143 e. oe of the above Statistics 211 Practice Exam 2 19. O a multiple-choice exam, there are 5 possible aswers to each of 20 questios. Each questio has oly oe correct aswer. A studet, J, has ot studied ad must guess the aswer to each questio (you may assume that the guesses are idepedet of each other). J must aswer at least 10 questios correctly i order to pass the exam. The probability that J will pass the exam is a. 0.0011 b. 0.9994 c. 0.0026 d. 0.0006 e. oe of the above 20. The probability distributio for a sigle toss of a fair tetrahedral (four-sided) die is X 1 2 3 4 P(X) 0.25 0.25 0.25 0.25 The expected value of X is a. 1 b. 2 c. 3 d. 4 e. oe of the above 21. A sample survey a. attempts to acquire data from every member of a populatio b. attempts to acquire data from a subset of a populatio c. is the same as a samplig frame d. is the same as a cesus e. oe of the above 22. A simple radom sample a. is obtaied i such a way as to esure that every member of the populatio has a equal chace of beig selected b. usually requires that a samplig frame be costructed c. usually results i a sample that is represetative of the populatio from which the sample was selected d. all of the above e. oe of the above
23. The cumulative biomial probability P(X 4) correspods to a. the probability of gettig exactly 4 successes i our biomial experimet b. the probability of gettig fewer tha 4 successes i our biomial experimet c. the probability of gettig o more tha 4 successes i our biomial experimet d. the probability of ot gettig exactly 4 successes i our biomial experimet e. oe of the above 24. Which of the followig would result i a icrease i the width of a cofidece iterval? a) A icrease i b) A decrease i the stadard error c) A decrease i the cofidece level d) A decrease i the sample mea e) Noe of the above would cause a icrease i the width of a cofidece iterval 25. The Heart Associatio claims that 90% of adults over 25 years of age caot meet the requiremets of the Presidet s Commissio o Physical Fitess. A radom sample of 400 adults is selected. Fid the probability that at least 50 of these 400 adults meet the requiremets of the Presidet s Commissio o Physical Fitess. a. 0.1583 b. 0.8417 c. 0.9429 d. 0.0571 e. oe of the above