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midterm_solutions

# midterm_solutions - Stat 651(Winter 2011 Kaizar Exam 1...

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Unformatted text preview: Stat 651 (Winter 2011) Kaizar Exam 1 February 3, 2009 Name - SOLUTIONS There are ﬁve multi—part problems in this test. To receive full credit or partial credit, please be sure to show all your work. The exam is closed book/ closed notes. You may bring a single 8.5”x11” page of formulae to this exam. A calculator is allowed — a personal digital assistant or cellphone is not. The exam Will last for 108 minutes. Good luck! Question 1 (20 points total) The OSU faculty and staff newspaper “onCampus” posted the poll in Figure 1 on their website, and reported the poll results in the January 6, 2011 edition of the print newspaper, as shown in Figure 2. onesmmseou H; »‘ ' ~ :r f_'."__‘_"‘_‘"“‘f"_‘f """" Onli’n-e--pel:ltr Havewutaksn an {mime - _ ' :emesr'wtzzevr.thanmis ' ; we??? ‘ ’ Pernentae' mamammarameex is»?Q ﬁts‘ﬁaﬁl- -' writamme-gasa-mmm :. rs: wrta‘rn‘mxssfrsuremis- ’ r -» . , ' " _ . than‘tbls»; utter], -- .a- f??? Morethanrsa mar-\ihsgagoesr ,moliﬂis.ViSit oﬁmmpﬁ: " ‘_ 9985}??? r. , Figure 1: Online Poll _ Figure 2= P011 Report (a) {5 points}. Based on the report, what is the target population of the poll? 080 57%? ml dammit?) ' (b) {5 points} Assuming that no one participated in the poll multiple times, what is the sampled population? An‘jm who might W ﬂew [95/ ﬂit/(l Qﬂfwﬁﬂfoe If, (c) {10 points} What do you think is the most important nonsampling error for this study? Brieﬂy explain how you think this error impacted the reported estimate. U/lcpﬂ/ V ' 06¢ [AA/LP do “0+ Ugvngé’éj I Parﬁcm" mlif: 5M5. Since, “West; :WWM 4mm “no “ 4W5 su-rvﬁj‘S' requh m that [my Mud! ( MPWQW Question 2 (18 points total) A relatively new idea in survey design is to administer the survey via an online website, but invite survey participants via a paper invitation. One example of this is a customer satisfaction survey conducted by the Subway restaurant at Nationwide Children’s Hospital. For this survey, the restaurant takes a systematic sample of purchases and prints a request to complete the questionnaire at the bottom of the sampled receipt. The cashier verbally points out the request as she hands the customers the receipt. The request looks like this: Take our E-minute Survey at www,tellsubway.com and receive a free cookie. Keep your receipt and write vnur unique coupon code are __. Marx“ forge ‘ back and‘vésit SUBWAYgR‘ within 7 days and receive dcubie.pg nis on your. grenase! Offer avgiiahle fer a iimited ‘we at participating iocatrons.*#*** Host Order ID: 05W.g3hu (a) {6 points} What do you think is the biggest advantage of including a paper invitation? Brieﬂy explain. ~ E51351 cal: merging 50(er (s Wih‘ﬁt‘i Wm; whaééiﬁia, (Ail/um We. Erma» {admin is 37 \$662447 M1 We. ca ma ‘ 9&4):st Mama (b) {6 points} What do you think is the biggest advantage of including an online portion of the survey? Brieﬂy explain. £0315 , [whwa swivth need Wile. , Swimcﬁ Md 4/2; WMGML V348} I'Aeicfmsii/F . (c) {6 points} What do you think is the biggest disadvantage of including an online portion of the survey? Brieﬂy explain. Unﬁmommf - I 414' SWVICJ MN" 4"qu 1:3 IWHTA gaff} mkzme‘k amass. Question 3 (20 points total) The Columbus Police Department (CPD) has been installing trafﬁc light camera systems to identify and ticket auto drivers who fail to stop at red trafﬁc lights. When the system senses that an automobile has entered the intersection While the trafﬁc light was red, the cameras take a photo of the front and back of the car, as well as record a short video of the potential violation. At a later time, a police ofﬁcer looks at the photos and watches the video. If the ofﬁcer believes there was a trafﬁc Violation, the owner of the car (as identiﬁed by the license plate) is ﬁned \$95. The CPD annually evaluates the ofﬁcer assessments of the photos. For this evaluation, a supervisor reviews a simple random sample of all the photos taken that year and either conﬁrms the original ofﬁcer’s opinion, or ﬁnds an error. The goal of this study is to estimate the proportion of errors made that year. In 2009, the supervisor examined 200 of the 35,385 camera—recorded incidents. Of these, she disagreed with 8 of the original ofﬁcers’ decisions. For this problem, assume there is no non—sampling error. (a) {6 points} Estimate the true proportion of mistakes made by the original officers. ong’ 3 317’ 0.07 2.00 (b) {8 points} Estimate the standard error for your estimate in part (a). A _"\) zoo .7: ' n e0 6" O ,_ {333, ,M Mama/31 (c) {6 points} Are you conﬁdent that ofﬁcers made mistakes on more than 1% of the recorded incidents? Justify your answer. ,4 7% c3: covlci be Ceasivucf‘wii arc/ﬁz—(M/sﬁﬂ a: (mag, MM?) tag... I”... 75% Mai/me 474M:- 474 6%267'5 mate. york-later m “flmn I90. I 6 kiwi/Ag, is Hr‘CaSMabb good grafﬁti.“ (4,. N,_an&{ N'VL AN age rm swish 147,0. ' Question 4 (17 points total) A paint manufacturer has been experimenting with a new way of producing specialized paint on a very small scale. A customer may order as few as 6 one—gallon cans of paint. However, since this process is new, the paint in each order must still-be tested beforeit is shipped to the customer. In a particular batch of paint, it is only cost—effective to test the contents of 3 of the 6 cans of paint. The quality control specialist randomly selects 3 cans as they are ﬁlled according to the following plan. The specialist ﬂips a fair coin. If the coin is “heads”, he tests the ﬁrst, third, and ﬁfth cans. If the coin is “tails”, he tests the second, fourth and sixth cans. (a) {3 points} What is the name of this type of sampling? ' S sitmméi'c 54/2470] {46, ' [2 amt cage mt clots!” San/IP54?) (b) {6 points} What is the sampling weight of each can? 533%]: 31 53 SL’EZ/q’bi ’ - i ' :le TE“ 2’ , J “LT-H’v‘T/ﬁb v 2’ W, (i=2 41w e (c) {8 points} Suppose the coin comes up ” heads”, and the test results a hue of 4.5 for the ﬁrst can, 3.1 for the second can and 3.3 for the third can. Calculate the Horvitz— ' Thompson estimator of the average hue .‘ among all six cans. Question 5 (25 points total) The ice storms this week have been particularly challenging for those whose primary mode of transportation is walking, since many owners do not properly clear the sidewalks in front of their property. According to city law, each homeowner that fails to clear their sidewalk should be ﬁned \$100. However, the law is rarely enforced. City ofﬁcials claim that it would be too costly to enforce this ordinance. I The Coalition for Salted Sidewalks (CSS) believes that if the law was truly enforced, the ﬁnes would pay for the enforcement. To bolster their argument, they decided to conduct a survey to estimate the proportion of sidewalks that were not cleared within 24 hours of the end of the ice storm in the OSU campus area (excluding University property). CSS has access to a complete enumeration of buildings in this area (provided by the County Auditor). This list includes the type of property and the location of the property. In a small pilot study, they found the following results, broken down two ways: I number in sample {15 1 r with cleared walks Type population size sample size ' Business 18 (9, 070 @ . 070 Residential 8 0, I I 0, 095 Unoccupied 0 0 0 TOTAL 26 NeighborhOod population size sample size number in sample A A IA) with cleared walks 7D I (")0 University District (East) 8 0, 24' 01 20 Short North/ Victorian Village 7 0. Z3 0 v1 Clintonville/ Upper Arlington 11 0, 25 0, Z 0 TOTAL 26 (a) {10 points} Based on the pilot study, which variable (property type or neighborhood) would be better to stratify on? Explain why you made your choice in terms of how it will improve the overall estimate. «ILL vanish/iffy . r shhﬁ‘wf by, m'qiibwhwd ' Emma 05 4M3, “1PM, Vanimm «HAL Wit/yaw! Waﬁéd cﬁimmiw ma" ﬁe {profof/im 5:15” Ema/[fry (b) {15 points} In the ﬁnal study, 088 plans to sample 2000 properties. Speciﬁcally how should they allocate this sample? (Your answer should be numeric, not just descriptive.) Explain why you chose this allocation. g;s/Nv “gig/\$379001”): 9M0; N553“ =L/OM/o.b%z=/Zo,/5“ ' ,5; .99: , ; 4/3 S; ’n‘: %(WXW>“ O‘MH MKSK— #37 r O w 0 1:), W N ’ 32 it 74352] [0—)(6) "’ 0 L" M’ Nﬂym’l ,st:W ﬂalsm/[g7é/3 , Vii/a :ZOMCO’ 5 20’ /‘/.Z 45,13. 3 “K 7ZOﬂC) (/l/s‘lbﬂzg ‘ lacy a ﬁa’ﬂé) ; / ‘1’ Win / 3 nuczaaafo§ =-= 62> Wf M 4% Z ‘glogeye/I’AV'MS {lg/r“ gnaw. 0w amen :1: 4a» lea/:42; 2 s m wwwﬂga jamﬂmx/ M'A W4 (/96 Ne7mpm A’ﬂaaﬁym 7'? [914% “7,11 warm/'41:? ynznﬁl ; M75ﬂ5ﬁ/W) -= 2% W”? = 2| M505 M712 :W?7’ n,2 ; mag/0,79%} ...
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