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Sotunoss 2012 AP® STATISTICS FREE-RESPONSE QUESTIONS STATISTICS SECTION I Part A Questions 1-5 Spend about 65 minutes on this part of the exam. Percent of Section II score—75 Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. 1. The scatterplot below displays the price in doltars and quality rating for 14 different sewing machines. ® 80 ° & clen ,5\ 2 70 ° /3?\ pourT 5 . N J & B2 6012 *e g 50 p ® 40f—= . 0 $500 $1,000 $1,500 $2000 $2,500 e 15 o canvede pon-Ineal assoc Price (dollars) )y . blw FY\LQ & ziw\\l{\a ra\%\rxs . (2) Describe the nature of the association between price and quality rating for the sewing machines. (b) One of the 14 sewing machines substantially affects the appropriateness of using a linear regression model to predict quality rating based on price. Report the approximate price and quality rating of that machine and explain your choice. 2 $3200 3 65 ¢ wl\'M) (c) Chris is interested in buying one of the 14 sewing machines. He will consider buying only those machines for which there is no other machine that ha§ both higher quality and lower price. On the scatterplot reproduced below, circle all data points corresponding to machines that Chris will consider buying. 80 o) - af ° g 70 .z\ 60 [] (] g & < 50 . ° 40 . 0 $500 $1,000 $1,500 $2,000 $2,500 Price (dollats) © 2012 The College Board. Visit the College Board on the Web: www.collegeboard.org. GO ON TO THE NEXT PAGE. -6-

2012 AP® STATISTICS FREE-RESPONSE QUESTIONS 2. A charity fundraiser has a Spin the Pointer game that uses a spinner like the one illustrated in the figure below. A donation of $2 is required to play the game. For each $2 donation, a player spins the pointer once and receives the amount of money indicated in the sector where the pointer lands on the wheel. The spinner has an equal probability of landing in each of the 10 sectors. (a) Let X represent the net contribution to the chatity when oné person plays the game once. Complete the table for the probability distrbution of X. Conin buhon = $2 — (A///N'\’/\SJ P $2 $1 38 P@) o b .3 o | (b) What is the expected value of the net contribution to the charity for one play of the game? (c) The charity would like to receive a net contribution of $500 from this game. What is the fewest number of times the game must be played for the expected value of the net contribution to be at least $500 ? (d) Based on last year’s event, the charity anticipates that the Spin the Pointer game will be played 1,000 times. The charity would like to know the probability of obtaining a net contribution of at least $500 in 1,000 plays of the game. The mean and standard dev1auon of the net contribution to the charity i 92 lays of the game are $700 and $92.79, respectively. Use the normal distribution to approximate the probability that the charity Would obtain a net contribution of at least $500 in 1,000 plays of the game. b) Swptdys 2(.6)F ‘('35““8(")@ & 22 iy as—s IS 4;;;@ Pl e = SUD('?OD == 2,155 92,79 P(R7R.150) (T84 Y © 2012 The College Board. Visit the College Board on the Web: www.collegeboard.org. GO ON TO THE NEXT PAGE. -7

2012 AP® STATISTICS FREE-RESPONSE QUESTIONS 3. Independent random samples of 500 households were taken from a large metropolitan area in the United States 6 1he years 1950 and 2000. Histograms of household size (number of people in a household) for the years are shown below. \o\rf)e enovo ro /,SD‘“O v Number of Households Number of Households 120 601 40 Household Size in 1950 o) Lower center in 2000 3-% Peopla, vs, ()aop\e, in V85D Less varmaton ia 000 beco\vse, of Kvge clugler -5 PeoP\Q vs . A peap(e, in 1950, frore exdve rre Values (\o+> in Oso then 2.000. Q,OH\ af skamﬂ-g h‘gkﬂ but more so o 3000, ble less yauseal 4o herve Sveh high numbergof pesple (o) P atleasT loX vapu s W16 6 8 10 Household Size in 2000 (a) Compare the distributions of household size in the metropolitan area for the years 1950 and 2000. (b) A researcher wants to use these data to construct a confidence interval to estimate the change in mean household size in the metropolitan area from the year 1950 to the year 2000. State the conditions for using a two-sample f-procedure, and explain whether the conditions for inference are met. © 2012 The College Board. Visit the College Board on the Web: www.collegeboard.org. GO ON TO THE NEXT PAGE. -8-

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