Stats21_Purves_07F_Midterm2

Stats21_Purves_07F_Midterm2 - (10) 1. ‘\ \CA '2 For a...

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Unformatted text preview: (10) 1. ‘\ \CA '2 For a certain list of incomes, the average income is higher than the median income. All the incomes are positive numbers, and the units are dollars. Let x be the list. (a) Each income on the list is off the average income (average of x) by some amount. True or false: r.m.s. of amounts off = I (av [X2] — (average of x)2 3 No explanation required. (b) Each income on the list is off the median income (median of x) by some amount. True or false, and explain: _r.m.s. of amounts off =./ (av [x2] — (median of x)2 \ mm a a v as .5 \1 p (N. {Kw ‘, a” ‘ C‘.’ \‘G i; i 5 a a: (b) Vita umr’wwifi “"5” i if M * / - \ 4’ 7 f“ i 3:3? A I . r u p: 9‘” * af—tfim (la/Mylo, flig‘EiJ;{f€ «WE m i , a ti fin \ y ‘ p O V fin - Ii”: ;, was V ‘ SJ mast ‘w “ERAS kg’v’xfck guevw‘Q-‘f . Tug W k Via} r J . 1. (continued) (c) For the list x: r.m.s in (a) = $10,000 r.m.s in (b) = $10,440 (rounded to the nearest dollar) For the list x, the average income is higher than the median income. By how much? In other words, find the difference: average of x — median of x. a; / {i 2“!) mvéxzy 2 W1“) "x W: if a ,i E {*1 ' w a UAW r (wax. )~ TBgig/irz v ) K” Mw‘ffixi (10) 2. A small room contains 4 rows of 5 chairs: front of room 69 X ® . 69, X x x x x x )4 x x x x x x ,x. "X x back of room In (a), (b), (c) below, people enter the room one at a time, and the room is empty before they start to come in. The first person to enter is assigned at random to one of the twenty seats in the room; the second person to enter is assigned at random to the nineteen seats remaining; and so on. ‘ (You can leave your answers in a box looking something like: Ans = 19 x (17/107 X 6/94 x 15/150 X 29/780 x 3/57) + + more terms like that Remember to show your reasoning, though.) (a) 'l\2vo people enter the room. Find the chance they end up sitting beside each other. at J: 7 r f .w' w- , JR; \ ‘ 7 lg 73. "I .g, +«r ' _) O X an: 5" ' If) ./ ' sz- . I f g V r g Q g 1 f A M jaw 22v 4' ‘ ‘3‘ fl ‘7 7/ it 1 4/ ‘ I, 3 A , if ‘ my a . (b) Three'people enter the room. Find the chance they end up in the circled seats. :v 1! ~r’ : y, * .~ ,e’“ la ; / if: {C inawhfii’ 5" , x C “a”! J 6 a i X c a? m : g“ fl )5: C arm la 6; r: 11‘ c‘g 9” a l “a! a 5 '7 M i; 7M“! .4 a I M. 9:! if»: Q \ k)Cx_LI " (E, ,2” W“ " ‘ ’ 3i 4 ' l g i i X " x "L l C 4/, (c) Five people enter the room. Find the chance three of them (no more, no less) end up in the front row. _ WWW p Y ., i 4.... __A .i U "Mk L K r “l K . ii W “v i ‘” f l s [is 3 v Q g :1 3» l 5 WV l l I l . /' x q X --« \e ,— g “j” w gm l “30 l W? t 7 l E a" ‘ ‘ \v\ l a: j: X ché’ git???” Dz / 3r T f . "i C a???" 0% r” ‘ 5" XFX/V’x/Vl “N” M ’5 (5) 3. A gambler playing roulette (in Nevada) can make a section bet—for example, bet $1 on the numbers from 1 to 12 (inclusive). The bet pays 2 to 1: if one of the 12 numbers comes up, the gambler gets the $1 back, along with an additional $2. Otherwise, the gambler loses the $1 stake. ’ A roulette wheel at Nevada has 38 slots, in each of which the ball is equally likely to fall. The slots are numbered 0, 00, 1, 2, . . . 35, 36. Two gamblers, Ann and Bob, both like the section bet. Over a year Ann makes it 150 times and Bob makes it 300 times. It might turn out that: (i) Ann wins more than 45 times. (ii) Bob wins more 90 times. Check ( \f) one of the three options below, and then explain your choice. The explanation should involve little or no calculation. (i) is more likely than (ii). _, R X (i) and (ii) are equally likely. _ (i) is less likely than (ii). , r“ ‘ c l ‘ , ‘3 ms {in we: bd’li’: M V M N f r ' y f “g, r alb/ Wlnlfilh Covvrif‘lfitwé '§""0 A g 1 C; “ 7&1. a. (75%? f. 52:59:55; M ‘3; O ’3 3'” 97a “en’s?” g‘l; i493 5“ 1 t i E g at :2” mantis if flight? “at (if 6 atom: a? 19‘s? wisest? 2mm r s s (10) 4. The box below contains one hundred tickets, numbered from 1 to 100: HIE!!! Two hundred and fifty draws will be made at random, with replacement, from the box. On any draw, the number on the ticket might be between 40 and 60 (inclusive). Find, approximately, the chance this happens on 52 of the draws (no more, no les's). a ‘ .4 r , id ‘ U l taxman 1w M‘ f» filly“ m {"3 5W “I; $2} {:1 a f" big a ‘ EV] 5M4!“ r Y 93¢):g2‘3 \oo 4;; -« x—gESGr ”' 2 ‘:fig;; w vc2z5_uq if)?" n ’2‘ w? ‘9 -" x w u ‘5 1m!» HM (legume ow \S: l;“" is w ‘ffr ‘4; «v $79951“: ,, M r 3 {I "I («‘0‘ (5) 5. In the presidential election of 1948, the error made by the Gallup poll in its prediction of the popular vote was about 6 percentage points; in the election of 2004, it was 1.7 percentage points. True or false, and explain: The main reason for the better prediction in 2004 was that the Gallup organization used a much larger sample in 2004 than it did in 1948. i ,5 . t“ . n 2Q . are i» * gwyiv 92:2 wowl Vol/it“ , . s . i 91:34 an; «r 9 r a”? ’" W x '31:} '1 “.8 arm '1 (L L t Vb f A a a E ii " ‘- l ’ “‘+ - er say my :3; axial}: ; @‘g‘Wfill—“vt‘ M :1! worse 1 iii, JFK / be $1; a? a”, IS ' r 7/ L L ‘ f °' 5 I 4: 9: row.“ (*3. “angel ’}‘0 e/(VV‘ ma’f (4 Q r ‘* . as??? {4 a “’ L/flf «if e r [x r! . f i In w r- ; ‘fitg , at: all/Kl bmdc’ 7L airbag?“ 4W" whim “(Siig 3&3) j} (O . (10) 6. A survey organization takes a simple random sample of 500 residents from the Bay Area, ’ and asks everyone in the sample the following question: “Between now and 2025, California’s population is estimated to increase by 9 million people from 37 million to 46 million. On balance, do you think this popu- lation growth is a good thing or a bad thing, or does it make no difference to you and your family?” To answer, please choose one of the four options below. (i) a good thing (ii) a bad thing (iii) makes no difference (iv) don’t know. In the sample, 65 people chose (i); 280 chose (ii); 135 chose (iii); and 20 chose (iv). (a) Estimate the percent of residents in the Bay Area who think the population growth described in the question is a goodcthing.“ ' -— l a u! KL} E: X foe ‘13 fife Z '3. ‘ ‘ if (b) Attach an SE to the estimate in (a). km . g _ ,f “In : tag“) {’65: i wag : 39 S’QUR ‘S. 5 g , , if m *’ e“ ? >5, 1 232‘: K419) Di A «$530 MON J «an ,, X N /' /‘ !\ (A. 9 'o (c) The range from / O l/C’ to 6 /° is an approximate 95%-confidence interval for the percent of residents in the Bay Area who think the population growth (describ- ed in the question) is a good thing. ( A .t O. a l r! ., ,. ‘2: 5 l r" *“ fl «(.7 1A “HA a [s Ur; :‘ é :; gm m, 2% ,Ma (Note: This problem is loosely based on a survey described in an article in the San Fran- cisco Chronicle of Thursday, January 5, 2006. The survey in the article was carried out by the Public Policy Institute of California. The numbers 65, 280, 135, 20 given in problem 6 reflect accurately the findings of the real survey.) ...
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Stats21_Purves_07F_Midterm2 - (10) 1. ‘\ \CA '2 For a...

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