AP Statistics 2009 Free-Response Questions Form B

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AP Statitic 2009 Free-Repoe Quetio Form B The College Board The College Board i a ot-for-profit memberhip aociatio whoe miio i to coect tudet to college ucce ad opportuity.

Each year, the College Board erve eve millio tudet ad their paret, 23,000 high chool ad 3,800 college through major program ad ervice i college readie, college admiio, guidace, aemet, fiacial aid,

1 AP Statitic 2009 Free-Repoe Quetio Form B The College Board The College Board i a ot-for-profit memberhip aociatio whoe miio i to coect tudet to college ucce ad opportuity. Fouded i 1900, the aociatio i compoed of more tha 5,600 chool, college, uiveritie ad other educatioal orgaizatio. Each year, the College Board erve eve millio tudet ad their paret, 23,000 high chool ad 3,800 college through major program ad ervice i college readie, college admiio, guidace, aemet, fiacial aid, erollmet, ad teachig ad learig. Amog it bet-kow program are the SAT, the PSAT/NMSQT ad the Advaced Placemet Program (AP ). The College Board i committed to the priciple of excellece ad equity, ad that commitmet i embodied i all of it program, ervice, activitie ad cocer The College Board. All right reerved. College Board, Advaced Placemet Program, AP, AP Cetral, SAT, ad the acor logo are regitered trademark of the College Board. PSAT/NMSQT i a regitered trademark of the College Board ad Natioal Merit Scholarhip Corporatio. Permiio to ue copyrighted College Board material may be requeted olie at: Viit the College Board o the Web: AP Cetral i the official olie home for the AP Program: apcetral.collegeboard.com.

2 Formula begi o page 3. Quetio begi o page 6. Table begi o page

3 Formula (I) Decriptive Statitic x x i 2 1 x x x 1 i p ŷ b b x 0 1 x x i y y i x x b 1 2 i b y b x 0 1 r 1 x x y y i i 1 x y b 1 y r x b 1 2 y yˆ i i 2 2 x x i -3-

4 (II) Probability PA ( B) PA ( ) PB ( ) PA ( B) PAB ( ) PA ( B) PB ( ) EX ( ) x xp i i 2 Var( X) 2 x x p i x i If X ha a biomial ditributio with parameter ad p, the: PX ( k) p k (1 p) k k x p x p(1 p) pˆ p pˆ p(1 p) If x i the mea of a radom ample of ize from a ifiite populatio with mea ad tadard deviatio, the: x x -4-

5 (III) Iferetial Statitic Stadardized tet tatitic: tatitic parameter tadard deviatio of tatitic Cofidece iterval: tatitic critical value tadard deviatio of tatitic Sigle-Sample Statitic Sample Mea Stadard Deviatio of Statitic Sample Proportio p(1 p) Two-Sample Statitic Differece of ample mea Stadard Deviatio of Statitic Special cae whe Differece of ample proportio p1(1 p1) p2(1 p2) 1 2 Special cae whe p1 p2 p 1 p Chi-quare tet tatitic oberved expected 2 expected -5-

6 STATISTICS SECTION II Part A Quetio 1-5 Sped about 65 miute o thi part of the exam. Percet of Sectio II core 75 Directio: Show all your work. Idicate clearly the method you ue, becaue you will be graded o the correcte of your method a well a o the accuracy ad completee of your reult ad explaatio. 1. A gaolie price have icreaed i recet year, may driver have expreed cocer about the taxe they pay o gaolie for their car. I the Uited State, gaolie taxe are impoed by both the federal govermet ad by idividual tate. The boxplot below how the ditributio of the tate gaolie taxe, i cet per gallo, for all 50 tate o Jauary 1, (a) Baed o the boxplot, what are the approximate value of the media ad the iterquartile rage of the ditributio of tate gaolie taxe, i cet per gallo? Mark ad label the boxplot to idicate how you foud the approximated value. (b) The federal tax impoed o gaolie wa 18.4 cet per gallo at the time the tate taxe were i effect. The federal gaolie tax wa added to the tate gaolie tax for each tate to create a ew ditributio of combied gaolie taxe. What are approximate value, i cet per gallo, of the media ad iterquartile rage of the ew ditributio of combied gaolie taxe? Jutify your awer The College Board. All right reerved. Viit the College Board o the Web: GO ON TO THE NEXT PAGE.

7 2. The ELISA tet whether a patiet ha cotracted HIV. The ELISA i aid to be poitive if it idicate that HIV i preet i a blood ample, ad the ELISA i aid to be egative if it doe ot idicate that HIV i preet i a blood ample. Itead of directly meaurig the preece of HIV, the ELISA meaure level of atibodie i the blood that hould be elevated if HIV i preet. Becaue of variability i atibody level amog huma patiet, the ELISA doe ot alway idicate the correct reult. A part of a traiig program, taff at a tetig lab applied the ELISA to 500 blood ample kow to cotai HIV. The ELISA wa poitive for 489 of thoe blood ample ad egative for the other 11 ample. A part of the ame traiig program, the taff alo applied the ELISA to 500 other blood ample kow to ot cotai HIV. The ELISA wa poitive for 37 of thoe blood ample ad egative for the other 463 ample. (a) Whe a ew blood ample arrive at the lab, it will be teted to determie whether HIV i preet. Uig the data from the traiig program, etimate the probability that the ELISA would be poitive whe it i applied to a blood ample that doe ot cotai HIV. (b) Amog the blood ample examied i the traiig program that provided poitive ELISA reult for HIV, what proportio actually cotaied HIV? (c) Whe a blood ample yield a poitive ELISA reult, two more ELISA are performed o the ame blood ample. If at leat oe of the two additioal ELISA i poitive, the blood ample i ubjected to a more expeive ad more accurate tet to make a defiitive determiatio of whether HIV i preet i the ample. Repeated ELISA o the ame ample are geerally aumed to be idepedet. Uder the aumptio of idepedece, what i the probability that a ew blood ample that come ito the lab will be ubjected to the more expeive tet if that ample doe ot cotai HIV? 2009 The College Board. All right reerved. Viit the College Board o the Web: GO ON TO THE NEXT PAGE.

8 3. A Frech tudy wa coducted i the 1990 to compare the effectivee of uig a itrumet called a cardiopump with the effectivee of uig traditioal cardiopulmoary reucitatio (CPR) i avig live of heart attack victim. Heart attack patiet i participatig citie were treated with either a cardiopump or CPR, depedig o whether the idividual heart attack occurred o a eve-umbered or a odd-umbered day of the moth. Before the tart of the tudy, a coi wa toed to determie which treatmet, a cardiopump or CPR, wa give o the eve-umbered day. The other treatmet wa give o the odd-umbered day. I total, 754 patiet were treated with a cardiopump, ad 37 urvived at leat oe year; while 746 patiet were treated with CPR, ad 15 urvived at leat oe year. (a) The coditio for iferece are atified i the tudy. State the coditio ad idicate how they are atified. (b) Perform a tatitical tet to determie whether the urvival rate for patiet treated with a cardiopump i igificatly higher tha the urvival rate for patiet treated with CPR. 4. A maufacturer of toxic peticide graule pla to ue a dye to color the peticide o that bird will avoid eatig it. A erie of experimet will be deiged to fid color or patter that three bird pecie (blackbird, tarlig, ad geee) will avoid eatig. Repreetative ample of bird will be captured to ue i the experimet, ad the repoe variable will be the amout of time a hugry bird will avoid eatig food of a particular color or patter. (a) Previou reearch ha how that male bird do ot avoid olid color. However, it i poible that male might avoid color diplayed i a patter, uch a tripe. I a effort to prevet male from eatig the peticide, the followig two treatmet are applied to the peticide graule. Treatmet 1: A red backgroud with arrow blue tripe Treatmet 2: A blue backgroud with arrow red tripe To icreae the power of detectig a differece i the two treatmet i the aalyi of the experimet, the reearcher decided to block o the three pecie of bird (blackbird, tarlig, ad geee). Aumig there are 100 bird of each of the three pecie, explai how you would aig bird to treatmet i uch a block deig. (b) Other tha blockig, what could the reearcher do to icreae the power of detectig a differece i the two treatmet i the aalyi of the experimet? Explai how your approach would icreae the power The College Board. All right reerved. Viit the College Board o the Web: GO ON TO THE NEXT PAGE.

9 5. A bottle-fillig machie i et to dipee 12.1 fluid ouce ito juice bottle. To eure that the machie i fillig accurately, every hour a worker radomly elect four bottle filled by the machie durig the pat hour ad meaure the cotet. If there i covicig evidece that the mea amout of juice dipeed i differet from 12.1 ouce or if there i covicig evidece that the tadard deviatio i greater tha 0.05 ouce, the machie i hut dow for recalibratio. It ca be aumed that the amout of juice that i dipeed ito bottle i ormally ditributed. Durig oe hour, the mea umber of fluid ouce of four radomly elected bottle wa ad the tadard deviatio wa ouce. (a) Perform a tet of igificace to determie whether the mea amout of juice dipeed i differet from 12.1 fluid ouce. Aume the coditio for iferece are met. (b) To determie whether thi ample of four bottle provide covicig evidece that the tadard deviatio of the amout of juice dipeed i greater tha 0.05 ouce, a imulatio tudy wa performed. I the imulatio tudy, 300 ample, each of ize 4, were radomly geerated from a ormal populatio with a mea of 12.1 ad a tadard deviatio of The ample tadard deviatio wa computed for each of the 300 ample. The dotplot below diplay the value of the ample tadard deviatio. Ue the reult of thi imulatio tudy to explai why you thik the ample provide or doe ot provide evidece that the tadard deviatio of the juice dipeed exceed 0.05 fluid ouce The College Board. All right reerved. Viit the College Board o the Web: GO ON TO THE NEXT PAGE.

10 Probability Table etry for z i the probability lyig below z. z Table A Stadard ormal probabilitie z

11 Probability Table etry for z i the probability lyig below z. Table A (Cotiued) z z

12 Table etry for p ad C i the poit t* with probability p lyig above it ad probability C lyig betwee t * ad t*. Probability p t* Table B t ditributio critical value Tail probability p df % 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% Cofidece level C -14-

13 Table etry for p i the poit ( 2 ) with probability p lyig above it. (χ 2 ) Probability p Table C 2 c critical value Tail probability p df

Midterm 1 - Solutions

Midterm 1 - Solutions Ec 102 - Aalyi of Ecoomic Data Uiverity of Califoria - Davi Jauary 28, 2010 Itructor: Joh Parma Midterm 1 - Solutio You have util 10:20am to complete thi exam. Pleae remember to put your ame, ectio ad