/ Exam 2 Math 104 Fall 2015 Myers For full credit, please show all of the steps necessary to arrive at your answers. You may use scratch paper to work out your responses, and then write them neatly in the spaces provided here. You may use a calculator or GeoGebra and two 3.5 x 5 inch notecards. 1. Fill in the blanks. (a) The area under the normal curve between -1 and + 1 is about 63, 17! (b) The area under the normal curve between -2 and +2 is about q 5, L/5 '/. (c) The area under the normal curve between -3 and +3 is about q q,73 f 2. When should you not use r to summarize the relationship between two variables? 3. What is the regression fallacy? \~ ~rv5s\q~ ~~\\~~~ ~~ ~ V)V\Q.;V') -\~ v--e~r e.ss\~q1\ er-fe.u\- ~o.~t-'i ~ \~U l \aj\i-~,:t""f ~ \,,,-\\c, r 1~Q. \-\~"" vj.r,\\.(, ~(.l 9n>1.lf ~1l!LS lj..l",rst) ~ \1'~s ~ ~ ',\-$ :AAw~'I1~ -~9.f:.. +~.d\v\ -t~ r'l)vet;;sr~~~jv\ ".. "tt. " Sr e.1)(g..v~'qj'(,! '~ (.). (pj50~'5 \1\ "\'e~ l~ \,...,CJy\~~i'\;"'\ ~ ~\r Se-Ul"t"- 4;-",-'\- \!j wo,$<l, ""(ANA, ~,\" ~t.o "'~ \0... ~\~~ ~ ~(J-.~. -tcs+- does \oe \-kr OY'\ -\-\r\{i,r 1 L&.. -\-e5\- ~V\~ j ov.:\'t~~-l\ ~ ~~!~ W(J>..~ b~c{foo~ ~\~ \~ ~SoV\ WOtS OV'U' (_~V\~\d~ V\-t a(w ~ ~ ~ "la)v\tc""' \.. S VJ~J ~ (}, d \A.)0'l"i~ ov,\ \~(j. lc~. 1-.~;t -\-0lS,-,,-,o~tc\ \90 LA ~~l'es-sto~ ~\\(},t~.
4. Why do you have to be careful when interpreting ecological correlations? b~c-ctu5~ t-hey af"'e booe d on r'qree o()d overobe.-6 V"i h; ch hid e t-h e. e p r-e cd DI n d fy)ot< e t-h e C'o"'r~t':1 Cf+iOf)'O beefy) lo.l"eer t--hc..'")n "",,,hot r-he y ~ct--uall,/ c::tt... e 5. What does the Central Limit Theorem say? Nhe() dj'a""itt3 cr+ rclndorn ""I,...eplac~me()'t, +he. probob;i;t-y h'i t1t-o~rof(l -for +ri e 61..\rfI V'J\\t FD~\OV"'i +-h~ r")or-mol c-u,'vel re-30f'dle66 if t-h e cdn+-errt-~ e:..f' box clo('li+. - h ;0+0 5ro(Y\ ry'iqs'f - +h e_ d 00 V'4~ rnw6t be i (\ oh::tndd...-d i...t ni'h~ v;::)e let r-q~ enouab 'V o
1 \ 6. In a large statistics class, the correlation between midterm scores and final scores is found to be nearly 0.50, every term. The scatter diagrams are' football-shaped. Predict the percentile rank on the final for a student whose percentile rank on the midterm is A~551J-fh ; V'-fV 4, () 0 r Ih V'--\ ~ S1-c<1u.,{\6V\ o~- s C0r--,a.~ _1iJ~ I ~_, I ~Yo (a) 5%, 0 o 'N L I I \ ( r:t \Y2,r:Qii\T\ I.e r-.<:_"k ::: ')/,0, ~ S1-J:Adu-('d. \AD ItS) l.~ /\05' )j, I i ~~, ~~ v \ lfw_ 5~efH- 5cof\ed ' I. b5 (J~nib bejb{;0 ~I{J Oil tn_ (VI'\"j;- errtyi 'On +N -RAAt hc>l i5 Lite} -to S(t>~ «s «/,(,5 r'-r 6, 0).5' ()//~t-s h0b4l o..v-elajq 2=- 0,0d-.5; p-e-u' c en 4-; I e (b) 50% ~7, :,:t. +-- GOll.{~l '~ o.y\ C\_ ~?- ',I" =- 5~, 05% lmk =- )- s-q, bc;o;o :;;'0,-b% ~- o '5[)/-; ~bo\)' _ (}_1.J'er~<::'- OY\ -t/ae_ )'>1;j t<efp'), He (5 L i ~~ O~6 X 0 -:-' OSDs cj,ov'f_' (}.lj.-u'tl1!in +he A-"cd as W-eJ(, J k: <,. p-e r c e(1-h I.e r AI) Ie 0 f) -)-0.e _g- (\t:\.1 (,0 () 1.(-1 j b-e S'0 % 1'/;,I (c) unknown ~>!'~;-~:, ",,,. ', ':i.: ':;~/!I~ii ~\;)~~~> ',_' ~ 6~d~ft~" (Y) ~'J,t~r~ 600~ C<;, (71;05+ If{i~'.t; "~~,.'~,~rd,;;~\'.,.,:;'.,,' _ ~,~ : 'f...,.j':',.:. ':~,. )"" ~",:.~,J.'~:'.' ~ vwp~~; kpm/;e t0at:: ~ ttts2 fo;hq- o~ yj~~:,i' ~~t:~;~~!~~ 9L{f If'-e. ' '1'.'.: 'J-.l \ ti L.L ~ 7'-" II ~.Ji'\IA!) t{"i:,'.f:t!:,c,fff\tlj~ i,r_,n1,h; 61\ wl'fh. t-rt I, t\:i!'~5:" VLe,-' /':1,". \JW't'J\ V'''C / :.~.'i'",',..!,' ".'," (, -, t-~ :, ~~l~' 1$' l~!~e(d; +D b-e_ ~~)d ~to.".,,,', ;d~:''',' 7. In a survey of ~Igh-$chool students, a positive corr~latlon was fo:uri4: between hours sp,ent per we~k doing homework, an~ sc,oreson,:~st~haii~aj~ed achievement tests. The investigators concluded that doing homework helps prepa,re students \9r thes~ tests. Does the con~lusiori.:'toilow fiom t~'e,d~~ir, Answer yes or no, and explain, briefly. '..h ' Nn, A fb5?~h~ 'a5sdv\~f;()t'\ ~0e_s het-' )I'l(\flj' ccitstx.;h()n, he>, n I ('l -t-ktvt,, C6{_,(/LX :5+(,\~aP1+"':) +-0 TlA0VLt 6ou..tct IZ- (A(/ \171;(-11.&-,"'6 ~(Vt-'DIS, b Q " stu'<il Y'l'eo f\-q_ -h ~ cm\ d- hol'vl e>liork as well q s +0 clo (A>-e)J. 0(\ 5~Ad c"-{~\ ied +est-s,,.,.; [0
/ / 7 8. True or false: A student who is at the 40th percentile of first-year GPAs is also likely to be at the 40th percentile of second-year GPAs. Explain briefly. (The scatter diagram is football-shaped.) J=.ctl-se.., Be_Co. vse.~ +~ll_ 1f"2_'jlf"e.. S'S-ioVl ~f-k(.._+-) i+- ;"3 LkeJj +kcd-- f'e.ofle.- ivl +h.e_ (ow~ h~l.p v-p o f ft5 \IV ; 1I \ 9. Match the correlations with the scatter plots. C)-O.30 Match the correlations with the scatter plots. '------------------ -------
10. A gambler plays roulette 1,000 times. There are two possibilities: (i) Betting $1 on a column each time. (ii) Betting $1 on a number each time. A column pays 2 to 1, and there are 12 chances in 38 to win; a number pays 35 to 1, and there is 1 chance in 38 to win. (a) What is the gambler's expected net gain for option (i)? - \ - fjy-f,.1cf.rli:l vcdue-- ~ (ttotrow.3) (O-NB of Icox) =: 'OCX) (tg Cd -,~ -+2.6 '-1)) -=- \.0;::)0 [-0, 0526} '::-$ 62,63 (c) What is the gambler's expected net gain for option (ii)? ~- 30 -I I -hc~ t s -=r -1lc\cJl,-{J) eji. c-lw( 'J()\\ve---:;; 0-dfOW~) (on3 of bw) V =- \ COO (tg C~ 5 -r 37 (-I)) ) ::: ICOC) C -O,()~'(t). -c; -11 '52,(;3
5 (e) True or false and explain: The chance of coming out ahead is the same with (i) and (ii). p;/o-& ' 8ftro"", (1') : ~ 2>Q-l~ >Nia c~ ~ a~ if ~ ~ ~ t.?e..j '1l1j{VJ of J I <It le-«df,7. -------f,,_;;:..:..:..::::... :-L.-~..L..L_ '-I -)3 '5 I 1he:rf vv.:1 vi ~, ~ e. 4lt C:L, t:y1 G e e.yr~~ ~F :,-(-53J=S4,,L-.e_ 0~St fk "'oy-o { {OcL.1e, g (ves G(J' /r I.L~ \V/f~ tl(_, Sv_. L,v/J ~ 73, g} % c~~~.j LeJ~..../I:~/'_, /,2,$ S.[.1 tize_ 6recfe4 Va!/}{(_ J 100-7-71 2'::;' ~ Z.'I '3 ~.-... I B, 5 -T. ~ j-lto- (~ ct j81~:; 70 Z: - C~~c.e.-. at C-<r-I""J ojt ~h.e.et 0( I Iso> ~ Z3. S 5' ~ -=7-6'" 4 2 TL.ere-- Cs' (3~ ~ C< 2), 5 ~ % tl.c- t2cree-teca ikt/vc ~ -53,. Il-j c~.,._,ee.. ().f i'-u. Sv-- Le/-.~ v-/{~i.--, o,.s 5 {*" fr--! I~.r:": ~<>-'J 0' ie.n Co--/:'-'j 0""/-.c.: % cl~e of
7. 11. Consider the GeoGebra output below for the variables x = weight (in,\ pounds) and y = height (in inches). ~ r S D \-\...,.. 4~loq (~.(PcmJ qjo.o.t'> LA ~ m 1. +b m ---- ~ (a) Find the regression line for yon x. J ~ Dx d. q 1330'6 ~ j( ~ \'-z ~. q 'Z-4l~ ~ DOt{ 3 ~ 3 ~ -:;. 10.3075 ( lo.3d15 :: C043d3)(\l~,~9_1{4) t- b 17"_ (0 d ' slid) [~ :::.,o43d:->")( -do 2,51191 ~ ::-~-t- v: ~w~vtt (b) Use the regression equation to predict the height of a person that weights 225 pounds. ~ '",04?Ja?(1-I.-5) +-(q1., "5710) I ~ co. l;)_. 30 UAcAe,>] _ /1 (b) Write the five-number suminary fore) h49ht (d) In what range of heights do we find the middle 50% of the people.,...--. measured? ll,15lvlches lo