Sample Mid-term 1 - Fnstrueters: Duratlen: Cemmeree ease -...

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Unformatted text preview: Fnstrueters: Duratlen: Cemmeree ease - Camputer Augmented Business Etatlstiee Midterm Examlnatlen 1 rsian 1 ' Fall Term. 213411 T. Saltshury and GD. Weselewsky 2 hours Maxlmum Merits: 65 Ititleleher 13. 2001 Last Name: 553% Flrst Name: Seetien Number Student Number lnstmetlens: 1. This mtnatien has 15 pages and 5G quastlens- ‘r'eu are respenslhle far ensuring that year may at the paper is eempiate- Brlng any diserepa ney ta the attentian ef yam intrlgtlater. All questiens are to be answered an the aeeampanylng DMR sheet. Use at enty the MeMaster Standard Calculatnr [Caste 1x991} is pennttted. Tables are an the last page. G. Mutflple Chaise - Prahlerns HID-EH} TOTAL maximum 3. Thls exam must he handed In slang wlth the GIMP. sheet. The exams and the DMFt sheets 1will he aefladed tagether. flat: the DMR sheets wfll be marked. Please flll In the nude far your student number an the fllh'lfi'. sheet Emmi. cheek and deu hle cheek. Please read the DMR lnstmefiane an Page 2. mtlnued... 2011.3 Midterm blame 1. You are writing version 1 of this exam. Indicate this by answering a. for this CL question. You MUST do this correctly. Discrepancies will be investigated as possible attempts at academic dishonesty. section A. TruelFalse {2 - 251 2. It Is assumed that a sample contains all measurements in which the researcher is interested. Fr 3. As a population becomes large. it is usually better to obtain statistical Information from the entire population. F 4. Ftatioecaled data are considered to have the highest level of measurement. T 5. Nominally scaled data are considered to have the weakest level of measureo'ienl. T b. The larger the number of observations in a numerical data setr the larger the number of class intervals needed for a grouped frequency distribution. "T" ‘i'. The mean is a measure of central tendency. ‘T El. The Session 1ii'Il‘Indow Is used to enter data into lvlin'rtab. F 9. If A and El cannot occur at the same time they are called mutually exclusive. "'T 10. Suppose there are three events A. B. and G with probabilities: Pie]: = H.512]. PtEl‘l = bill]. FIG} = CLUE. else. A and B are independent: A and C are mutually explosive: Pie and C} = .El5. Based on the above. El and care independent. F tiff-5 n [1)? p {B} e 151(3) 11. The number of cars that go through the drive~in window at a local bani: each hour is an example of a continuous random variable. F 12. In a Bernoulli trial there are two and only two possible outcomes. T lb. The probability of success changes from tdal to trial in Bernoulli trials. F 14. The dishtbotion in which the mean and the variance are equal is the uniform distnibutlori. F, 3 continued... EDAE Midterm blame 15- The probability that a standard normal random variabler E. is below 1.95 is cares. i3 i? is r- ift ti) ~— “Tina—if 16. The probability.r that a standard normal random variable. I. is betwaen Lilli and sooaunsrss. 1” Hialssia'rtfissE—Jtirie 1?- The normal distribution approximation to the binomial works best when n is small. F 15. a numerical measure of a sample is sailed a sample parameter. 1: 19. As the sample size increases. the effect of an extreme 1.ralue on the sample mean beoomes smaller. ’fi' 2D. If the population distribution Is skewed. in most cases the sampling distribution of the mean can be approximated by lite normal dishibulion ifthe samples contain at least 3i] observations. "T 21. As the size of the sample is increased. the standard deviation of the sampling distribution of the sample mean fora hem-rallyI distributed population will stay the same. F 22. Fer a particular sample from a finite population. the sample fraction was listed as 13.115. If the sample size was T". the population size was 14D. ‘T 23. The mean of the sampling distribution of the sample proportion is equal to the proportion of the sampled population possessing the charactedstic of interest. T 24. The mean at ttte sampling dishibutlon of the difference between two sample means is equal to the difference bah-teen the means of the hen sampled populations. T 25. in Market Area A. Elite of the shoppers but.r Brand it toothpaste. In Mart-tat Area B. 40% of the shoppers buyI Brand I. Consider the sampling distn‘botion of ph-p; based on aspirates of iii] and 12D shoppers drawn from Market Areas A and B. respectively. The mean of the sampling dishibutlon is .3- F l/Mt’n'F'e 1 Ta _T|rb i ‘L'rr‘Ur :‘l' It continued... EUAE Midterm Name Sectien B. MultlpIe lt'.':heice - Basics [26 49} MUTE: ‘3? Reund yeur answer to match numbers in chelces. lll'l.'l'i~en reading tables, dc net lnterpelate. Fer example, reund veur ncrmal deviate 2.513 te 2.91 is match the avallable digits in the table. A distn' teaticn that chews the pflgflpf chservatiens falling within specified class intErvals is called ‘— . statiatlcal lnterence a sample a relatlve frequency distributicn a pcpulatleh a frequency distributien Health care issues are receiving much attenticn In bath academic and pclitical arenas. A scciclcgist recentlyr conducted a survey:r cf citizens ever fit] years at age whcse net wcrth 1's ted high tc twenty:I fer Medicaid but whc have nc private health insurance. The ages at 25 unlnsu red senicr citizens were as fellcws: $0 6162 53 6-1- 55 EE 63 63 69 TD ?3?374?5 TE Hi B1 31 52 EE 3? 39 9E] 92 Calculate the mean age at the uninsured senior citizens to the nearest hundredth Ufayear' >“2_ evalut‘rtn #11 tilt-.00 years ’15. T3110 years H.134 veers SLED veers none at the abcve 5 CDl'liil'lLle... EDAB Midterm Marne EB. 1il'iihich of the following ls MDT included as part of the cutout frcrn l'u'linitahs DESGRIBE command?r a. mean t}. median c. standard deviation 6: nmfle e. all of the above are included In the output. 29. If either event A or event El must occur. then events A and E! are said to he mI.rtIi.iall1.r exclusive. statistically independent. collectiver exhaustive. None of the above. agave 3E}. The following is the probe hiiitir distribution of the number of cameras sold by a store In one day. a flat 1 ~ F 1 o.1s cit-T 2 [1.20 H‘s-"0 3 [1.25 ['1 5.” 4 sea J73 5 0.15 :i S' E CLUE .30 Eel-E What ia the expected number of cameras sold per day? a. 31] 3.15 c. 11.25 d. DJET e none of the above is continued... EDAE I'vtldterrn 31. NEME If n = 1b and n = DJ, then the mean of the binomial distribution la DIE. 1.45. EDD. 14.29. 2.1fl. Irv-Tl- '- Wat—J" A oonlinuoua random variable to equally lilter to assume any value between 1 and Q. What is the probability that thla random variable will assume a value lzlortllee-enlianlflTl"?r i=ol £11 3’5 1:3 film epilogue?) = up. 213 none of the above Flnd P{-o-5<zco.o}. b.3530 I11 915 13.5515 0.3035 none of the above Qualfillf For some value of E. the orebabillty,r that a etandard normal variable is. below I la oaoao. The value of I la “0-31 r- 5» ofllo 3.31 T‘- A 1- ung- fl.31 = fl iflHD 1.93 [1.51 T oontinued... sass Midterm 35. name A sample at sea subscribers tc a particular magazine is selected tram a pcpulatlcn cf aces subscribers. lt‘I upcn examining the data1 it is determined that nc subscriber had been selected in the sample mare than case, the sample cculd nct hays been randcm. the sample may have been selected witheut replacement er with replacement. the sample had ta have been selected with replacement. the sample had tc have been selected withcut replacement- Whlch cf the fctlcwing statements abeut the sampling distribu ticn cf the sample mean ts incerrsct'? The sampilng distributierr is approximately nermal whenever the sample size is sufficiently large [flea-D}. The sampllng distributlen is generated by repeatedly tat-ting samples at size n and cemputlng the sample means. The mean at the sampling distributlcn is ,c. The standard datdaticn cf the sampling distrtbuticn is a. All at the abeye statements are tme. Fteccrds at an autcmcbite insurance ccmpany shew that 10% at its pelicyhelders were lnyalyed 'In an accident during the past year- A randem sample cf #00 palicyttclders is he be selected. The standard error at“ the sampling dlstributicn cf the sample pmpertien is _ Ti ‘— - It fit " TD D flflflflflfi (11H 5 A—(rjl 11 a BEETS _ Tr 1— I . at . {1135? ET: ’ “(7” 1-H} g ncne cf the abcye E ccnttnued... sflea Midterm 33. Ne me Population A has a mean at ir'fi and a standard dcvieticn pt 15. Pcpuleticn E has a mean cf 1nd and a standard deviaticn pf 2t}. Ccnsider the sampling distripullcn at s A — s E. cased ch samples cf size 1554 drawn from Pcpuleticn A and samples at size dfl drawn frcm Fcpuleticn E. The variance cf the sampilng dishihuticn will be .25 .1 ,J 31.3? §—— -- Fad—+6151- Halvrlfll-‘i-er as iii—“s av.1 ma ' Ur are ' 1' 14 Fern.r percent at the people in Pcpulelicn A and Bull-t. at these In Pcpulaticn El drive a Emigmde autcmchile. Gcnsider the sampling distdhuticn cf pi — pB based cn samples at size 115 and 125 drawn. respectively. ircm Pcpulaticns a. and E. The variance cf the sampling distributlcn l5 Mi} Tflflui' WERE mfl=11§ emu—"'13 H.3fl c.0514 e r g _ llifl 6 : L {it 1E). Jr Trish 1—1—53 flflflEfl Pe'Fe mg m“ __ one + an in? 115’ 5' centinued... Juan? gH-si'u flE=IDD £31110 mashemflre sons MidtenTr Hams Section E. Multlple choice Problems Hi] - 5D] MUTE: i} ll] lit}. 3; s. 41. eases eee®e Round your answer to match numbers in choices. 1.i'u'hen reading tahlesI do not lnterp-oiate. For eitampler round our normal devlate 2.913 to 2.51 to match the avallahle digits in the table. The numbers 1. 2. E are a population. The 1«variance of this population is: .5 1+1+L, 2. [it—sitar 11—3. "“ - l JR”- —3' = 3 g :: —— 4-5T 3-15 ._ ‘T-t i4 '51 3-12 —'— 5.24 3 The prohahllily that house sales will increase in the next 6 months is estimated to he D25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 034. The prohahllity that house sales or interest rates will go Up during the next it months is estimated to he ELSE. The protestillltgi.r that bath house sales and interest rates will increase during the next ii months is: gm Wei-=15” tithes smug-.3121 iii: mm = mm Pitt. ~ FittclE Elm amt =t1fti’t'urvsflttn1‘) none of the above The number ofway's 4 ohgecta can he chosen from a set of T is: 3443 ’1'} _ Li— .5: as “r ’ tit-fist fifisjfigfsi 21D 12D noneoftheahove It] continued EDAB Midterm Name 43. A t's'in'lplengluI has a new preleet under vva1.r anti selects flve exeeutivea fer a transfer trem their eun-ent jeba. a. repert had suggested that T5% at all exemtives in this eernpanv weuld like this new ieb. What is the prebabfiitv that exeettv three ef the five aeteeted Iii'tfl their new jeb'? m 1 F Tl. ‘- ."l f i a. 0.0204 b. [1.4219 . 3 CE? erase PM???) 1 311. 1.73 L131 ease? ‘ - e. eases Let it be a hen'nailv distributed rendern variable with mean 100 and standard deviatien 20. Find it such that: Fit tflixtx'FflJfl. "6 filij €110 FEIWEXEHUFPKDEZEHZE . 12a =Fihé15,3'j:11e”f .3 El. T.H~=.ifiil3+.l=_lall5—' bH‘LZagl E 124 _tlxflgflhgslgeigb+‘slxlb 45. The en—llne aeeeas eernputer service industry.r is grewth at an extraerdiharv rate. Current estimates suggest that enlv 200i. ef the heme-based eernputers have aeeess te en-ltne sendees. Thls number is expected te grew quieth ever the next five years. Suppese 25 needle with heme-based eemputers were randernlv and independently sampled. Find the prebabilitv that fewer than half ef these sampled eu rrentlv have eeeess te en-line aerviees. Lee Ifii‘fl mtg: neat m. Eire--35? if Hm I]. e. uses 1 , a. bass. fie-5T : 13:4: 10 e- 0.000 m 3 ii seas Midterm 46. Name The amount of time it takes to complete an examination has a skewed-left distilloutioh with a mean of 55 minutes and a standard deyiation of 3 minutes. If 64 students were randomly sampled. find the probability that the sample mean of the sampled students exoeeds 1'1 minutes. 1 E— : :_ 1:: t " “ Approximatelyt] “M L3 g E m" E f]; 3031 5 >5 so mat-e oases r 1/“ :. t3; if; _ .-_ 2 _r ] oars: "_ s at?» m Approximately‘l 'F [x “tr—[1‘3 :- ‘P ('1 Hr. 'Tt-laf : F. a E :13) Reoords of an automobile insurance company shoii'ir that 10% of its policyholders were inyoiyed in an aooident during the past year. A random sample of son policyholders Is to be selected. Suppose the oompany has a total of ssoo polioy holders. The probability that the sample proportion of polioy holders inyolyed tn anaooldentlslsssthanfl‘ittis . szv'i “:1'Jt'BD fill—"2.3110 fl—n—nm :EILhL-DE—T JILL-ML ossts fit ' 150“ 0.3er m L‘rr-F \tflt} s at 9W H a 5'1 J; View t}.i]?35 r _ : 3 t ‘tt‘ — h 13:1 a flaws Egg“ #lgfl: 3,1_ Lesa. stats-m 3373 sea: 3} MW' flflfiflfi _ 5 N_m _ F3 1‘ Hm, : ms EIF‘ELT'J Q" " ’i Mai '— oo s‘tfi-‘t ‘ Fteoords of an aUtornohiIe insurgnoe oomp/rfiy showt t 1 “it: of Its po ioy lders were involved in an aooioent during the past year. A random sample of AIDE! polioyholders Is to be selected. The probability that the sample proportion of polioy holders inyolyed in an aooident is between 9 and 10% inolu she is - | arses W11" “‘1': UCDD 2M Mldterm 49. assets 5!]. Name Researchers believe that the amou nt of time in hours per month spent watching television by children ts an approximately normally distributed yarleble in each of two geographic areas. The population means and standard deuletitms are as follows: _ E .r't'L “— " i — so Standard m '4 1 E inf “r (iXqu H E) Area Mean dayiation melt/17mm}? W e tt'o—Fpa so=sfl flay—“'13 :fle_ 3—1:!ng A 190 2;“ 4t] :s'fl 6, h {1 ET “mi L '- _E " H + L t. -— :l-r — “it ‘3 on an: ago i Suppose that independent random samples of she a; = 4i] and on = ED are drawn from Areas A and B respectively. What is the probability that the difference between sample meansI s y - s a. will be greater than at} hou rs? _.— 1- 3 — osm ifliLKfl-XQ 5312*] : Pfil 3‘ w 13%} cases c.3413 : Ptlhih D3413 1 _ p.153? ‘5'- 3m?“ Researchers with an oil company belieye that the proportion of its credit card holders who make at least one out-of-state purchase during a year is the same {DAD} in two sections of the country. it they are correct. what is the probability that a random sample of 100 customers trom Section A and a random sample of 125oustonterstromSectionEwtllyieldsdil‘lienttnoedity-pa.5|reetertl1anillslil'iI iifi sTFEE‘iF my =iDD mfl=llh asset as on - new i ~ 333i: new {new} a toasting ’3 3': -“ Wigs mfll‘fi—E: illjilitx'i": o5 item “uni-:75 h _ itaitrmi if mm _-. TE~TE ' liq—Ht“?! TE, Sign—iced "#13" ET JV.— ‘nmh ‘ 1st: _ _ too + _:"tfi# HJLJEI? PH 13 continued... 1-. 1:1(2 2: 1%“ a '19 (2 bltFo) b-5-t‘t35'7 ZQAB Fa rmula Sheet Pawn} = pm} + pm} _ mm} Pmnm = I'm In) Pm} = Fall A: Pm} Rule I: :11 111 Run: 2: n‘ Hui: 3: nIIILrI-r}! Rule. 4": nlflrlin-rjlj 1: xiv-{11w}! P{x}= Iliflr]! nil-11:)”; E{x}=n1t; VARix]=m1:(1-Tt} Ew}=n: UP: 1:!1-113 fl fix1= w—i— where stsh; I1= fl :1: h“! 2 m _ EX. Eta-fl I“ h: Si: ['1 n 11-1 1': 2 1 1 - 5 l3'1 5: 15' g u I: _..._ u.._- - ._+_ r 3-- - I: _" __ I 4:3 “I- m a: ’-"’= n: * u: filaflfflrstddw. = E I 1' N—l I. I. I ...
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This note was uploaded on 12/21/2010 for the course STATS 2QA3 taught by Professor Buchanan during the Spring '10 term at McMaster University.

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Sample Mid-term 1 - Fnstrueters: Duratlen: Cemmeree ease -...

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