13 Questions with Answer Final Exam - Statistics | STAT 1040, Exams of Statistics

Download 13 Questions with Answer Final Exam - Statistics | STAT 1040 and more Exams Statistics in PDF only on Docsity! ---------Stat 1040, Fall 2006 Name: Final Test, December 14, 1:30pm-3:20pm Show your work. The test is out of 100 points and you have 110 minutes to finish. 1. The following was taken from a news website on September 10 2006: Alcohol use helps boost income Washington, DC (AHN) - According to a U.S. study, alcohol drinkers earn 10 to 14 percent more than non-drinkers. "Social drinking builds social capital," said Edward Stringham, an economics professor at San Jose State University and co-author of the study. He says,. "Social drinkers are out networking, building relationships, and adding contacts to their BlackBerries that result in bigger paychecks." (a) (2 points) Explain why this study MUST have been an observational study. 11rle.1 d1rl Oot ~ who drOJ\k. O,f\et who rh'J.., (\O~ cll'l'I\k.) So i~ mu.s f- be- obseJ'f) ()~bOf\a.t ­ ~ JU--Sf COtvlforeJ... me JJII\~rs fo ~- f\ 0(\ J,r-,' I\~r-). (b) (3 points) Explain why Edward Stringham's interpretation may be incorrect by suggest­ ing a plausible "confounding factor" and explaining why it is a confounding factor. Some- poss' b;/J;e-s.. SfrllS'5, Q~e..J d~ ". S~r-e.ss: RifhO{J5 s 1-~e.5j c.aM.S~ pflople. 10 ott,~k pu-hQ.P5 Phe...Cl. beJ/-eJ---~'f\q jcvbs ~ ossociaJ.eJ wdh IYlOffL stfe$~ A(jrL: peJ'hC{ps olrhi- ?'i.ople- o..«L.. More... II'~~ to hil\k ~j'let fJer-haps o(oter- pe.0p'e ~/\ol to fLaI'f\ fVl.ore-, . . G:U\rlJI: perhaps 'Mfll\ Qf't. Mo/'Q... ldw..y ~o cR.r;l\k oJ. we. k"ow MU\ I-el\d to Q..OJll More. ..J .. . . (c) (2 points) Does this study show that if you are a nondrinker, you can expect to earn more if you start drinking? Explain clearly using statistical concepts. ~O [ :h:s is O..J\ Ob5~LloJ-iOflCd sh.t.C£j Cl~ ~he, t,k;st-Q.naz. o.f fill) PO"~I btl'. co4o~.'J -fadors ~e<k.Q.S It l!Ytf'O"s;bI,. 10 ~ondiJ.J.e. . ()... COM.sol ('flJal-,O(\$hip, AS$oc,cJ-iCJ() J,o'?-S flOt- If\1plL( C.~lOt\. e-j' ;? ;f'5 a-{L bll-cau-5~ of jQ.l\kr) GhG\-~I" wh~ Of' 1101­ j0lA. olr-·If'Jk. w;1/ hewa.- ()O ~flLd" on ~ot.<J jW\cJ.-et--/ 2. CoQ10 is a somewhat controversial nutritional supplement that some people think is good for your heart. In one CoQ10 study, 23 men were randomly assigned to either a treatment group or a control group. Those in the treatment group took CoQlO supplements while those in the control group took a placebo. At the end of the study, the researchers performed a statistical significance test to see whether the CoQlO group scored better on a measure of "heart health" than the placebo group. The P-value was 15%. The researchers concluded that CoQl0 does not improve this meaS7J,re of "heart health" in men. (a) (2 points) What is a placebo? Why is it used? ,4 phce.bo IS s~me.-~;'j f-~Ovf- re.5~ble$ /--he-- 1-r~a1t'vle.ftf- kl- IQcJes t-hrL- QU-, iJll l'jI'Q£1 e",F I~ 15 u.S-eeL 50 f"'-aJ· p~op Ie. WI 1/ i\of- ~QW whic-h 31'CJUjO ~.a.:J CU€. 11\ Lb/"I\J) OJIJ. r-Q.acf.. fo fhe l:kt. r# (b) (2 points) Why were the men randomly assigned to the groups instead of having a· t~t physician decide who should get the CoQ10 and who should get the placebo? ~ f1..a.A~1;, e[IMIf\C\-1-e Po/'S0()o..( b,'ctS - f~'CI'CXI\S Mljh"'" pvJ- &.\~pel'-tI\f le.,'()I!..s Gf p(!ople 1/\ tv\~ ~WO (jt-OtJ.fS ~reof~f /rse1f·OJ\J the-fl We, t~vJ..& flof N2.-{ l'aJo~ c.oM~ ~e tfwuf· (c) (2 points) State the appropriate null hypothesis for this study. r\ LJ--Ll '. to Q I0 i, t-h e. scUY\ e.- a-·~ {-ftl e.. pia.c. e-b 0 W'I ~ r-e c;p~ C/f- ~6 f-hi J Me- a.s u.r€.- of 1\ he-off hfLav( ~h '~ (d) (2 points) If they used the usual 5% significance level, should they reject the null hy­ pothesis? Explain. No) fu~ wClt-JJ ~Clij ~ r~Je..c1- the. tllA.J\ ~p"th~sts kcctM.~~ t~v!-i('- P... vol! ~ Wo.s 15"&"1c, O-A.J we O(\~ f'Cj'eJ­ whe.-i\ the.- P... vCt-l...u. is Ie.?s thtx." .5'" (e) (2 points) Is their conclusion statistically correct? Explain. . IV 0) kCa.u.S~ W hQ..A W<2. -fOtII ~o r--Rj~c..(. the.. Yl vt rt 1AJt. &n() IJ- (,() l'\cl ~<L tho).· "~ is ~rtA..Jl . ( YI ~h; S case J 1-h~ 5CLI\Aple- was Ve:j SMcdl Lo t'\j 23 111"") SO 5ih ~ wl e.- po'5'5 ihie- ~n ec+ the- () Lc II ~ po u'e s ;s 1 ~oJ ~~ I i)JQ... j IAS f- el; &.11 'l-- htA-u e- CL 1j UIo'j'" S~Mp(e- '3ize.-- ~o ole.f-ed- i~. li 6. (3 points) All other things being equal, which of the following two samples will be more accurate, or will they be the same? Explain briefly. A. A simple random sample of 1000 Logan residents. B. A simple random sample of 1000 Salt Lake City residents. 1h~ shouJJ. be... o.bouf- +h~, SQMe be.-ccvuse- 1-he $(hMfle..s 'o.rQ. t"'~ so-me. 5i ze . 7. In a large statistics class, scores on the first midterm have an average of 75 and an SD of 10. Scores on the second midterm also have an average of 75 and an SD of 10. The scatter diagram is football-shaped and the correlation between midterm 1 and midterm 2 scores is 0.7. (a) (4 points) If a student got 85 on midterm 1, what do you expect them to get on midterm 2? '3"S-;5 10 roi"t5 a.1oo~~ QLJ~ro.:t- - th.cL~(5 IS]) oJoal/..tL CUI~, We- Q..-}cpe-d- ~IIV\ too be.. ,... h'M€.5 I <; 1) o.1ooVlL av Q. 01\- (VlI'JJerM 2.-_ ~') ,1 S.i) 5 doOvQ CLu-e-, - ". ~ , 7 S + .7(,0): 8"2. ~ ''7 LT; ):; .7. ) J;:: 125"+ '7(x) ,hI-' =- 2Z.fJ+-' J (85") 11\ e.rcep ::. o...v<?.'1 - Srofe lav€/() ~ 7t;"- .7(7/))=22.lJ .:= ~1.. (b) (2 points) Consider the student in part (a). Explain why you do not expect that student to get 85 on midterm 2. 1te... "tJf"'ftSslol\ ~C(- III trre.S51'Of\ +0 t~e. M('Cl(\ I') S 0S ~o.J' l-t SQfYi~O(\e. doe.9 w€-H 0(\ ~h~ tirst- fQst t.-Ve -e~ed­ thQM fO eta we.fl 01\ th.<L- s~co(\"d t-~5t hlA.J "ol- ~u" l-e a5 Wf.J(txS +''''e...j J.l'ot 0"- 't--[...~ ~I'S~. (c) (2 points) Find a give-or-take number for your answer in part (a). "'-MS V'rof'- ;: ~) S1)'"1 ;; 7. 14-. " .' ... '.-,.,.'. ,'.._... __ .... '_ .. ' 8. Sally's first grade class has 25 children (including Sally). Sally's teacher puts each child's name on a popsicle stick and randomly chooses 5 popsicle sticks, one by one, without replacement. (a) (1 point) What is the chance that Sally's popsicle stick will be the first one the teacher chooses? .;>. (b) (2 points) What is the chance that Sally's popsicle stick will be the second one the teacher chooses? (c) (2 points) What is the chance that Sally's popsicle stick will not be one of the 5 that the teacher chooses? (~)I 1.2 \( 1.-2)( z.. I )("2.0 ) l.}-S- l 24-) 23 n 2../ (d) (2 points) What is the chance that Sally's popsicle stick will be one of the 5 that the teacher chooses? 9. In certain countries, the game of cricket is very popular, and left-handed players often have a strategic advantage. About 20 percent of professional cricket players are left-handed. Suppose that a simple random sample of 200 cricket players is to be selected. (a) (4 points) The number of left-handed players in the sample will be about ~, give or takeS.lob or so. - ~1EJ 20] L Q~~y= ·21 2.00 S1) box = '4 EV£U-M - 200 C'2) = ~ Z; E W\1 :: JLOO (.4-) ~ S-, (.,f.c, s (b) (4 points) Estimate the chance that the sanlple will contain fewer than 35 left-handed 7. 35 ~o -.~%' .g-S I I ~ .- ...., .. ".- ..-_.:.,'., , .-. : .. ~ --':_"-"'0' 10. In a simple random sample of 124 students at a certain large university, the average IQ is 105 points, with a standard deviation of 8 points. (a) (8 points) Construct a 90 percent confidence interval for the average IQ of students at this university. l -I S'DbC/)( ~ ~ IO~+ 1,~~(72.) 3~WVI:: J,z.r.r (~)=gCf i·~. [05:!: 1.Z­ 5£a..ve- =- SS'Cf =-. '72 . I '2.-~ (b) (2 points) True or False, and explain briefly: 90 percent of students at this university have IQs inside the interval from part (a). FCAJSe. - +-h.cd- wow&. ktor I 0 ~± [. ",q-{ 8') ,12 (..I..Je.- k~.e.u.> {-hQ.- SCClr~5 .f'c,1[owecl the.. ACJ~Mct{ C-wv.e. 11. (10 points) In a PE class, a child gets an A if their pulse is over 150 beats per minute. One child has his pulse measured 10 times during the Class. The values are: 161, 156, 177, 161, e:tve-.:: _ -I .!i8, 148, 144, 156, 132, 152~ Assuming these are like a simple random sample of values of 1)5.5 this child's pulse during class, test to see whether the average for this child is 150 beats per minute against the alternative that it is over 150 beats per minute. Clearly state the null and 3D";: /['4- alternative hypotheses in terms of a box model, calculate the appropriate test statistic, find St)T- 1l..O the P-value, and state your conclusion. () u.U', a.v.e.r~ e...- I ~ I ~0 ettt: ~~ '> IS-O . +­ 12L-..-- ---.J( 5Dbo;< .~ SDSoJ\.1pIe, = SEsWV\ :: 5\0 ((2- ):: 37. 95':t '3 r S Ectve- ::. E ~ '5 I 1> 10 t-::.. (~~. S- - I S-o 6~~WQe.v'\. lOt3·8' CU\~ .lS2J~~ 10-1 -=..t:t -12­ LJe.. ~Cl.;/ 1-0 N2(e cJ- Jj (/ (. fr- 1- Jj O-P()O£Y>.AC"I'l \I T1'\,,-_ V\lA. Qo.- c...Ot'\c u..&JQ..V\O"..l n'\.e.. Ol:l Tjtf<::..V\ ~ MCtj j Uljf- be.. ChDf\C-L €..I'{or,