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# INTRO TO STATISTICS (QL)(SSS) STAT 1040

Utah State University

GPA 3.72

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This 15 page Class Notes was uploaded by Geovanny Lakin on Wednesday October 28, 2015. The Class Notes belongs to STAT 1040 at Utah State University taught by Juergen Symanzik in Fall. Since its upload, it has received 40 views. For similar materials see /class/230494/stat-1040-utah-state-university in Statistics at Utah State University.

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Date Created: 10/28/15

Statistics 1040 Section 006 Quiz 1 20 Points September 6 2002 Your Name M FPPp26 7 4 Question 1 Observational Studies and Experiments 12 Points According to a study done at Kaiser Permanente in Walnut Creek California users of oral contraceptives have a higher rate of cervical cancer than non users even after adjusting for age education and marital status Investigators concluded that the pill causes cervical cancer Answer the following three questions 1 Is this a contoll ed experiment or observational study Circle your answer 7 a This is an observational study the patients chose to be on oral contraceptives 2 Why did the investigators adjust for age education and marital status Age education and marital status are variables that are known to have associations with cirvical cancer and pill use They adjusted for these variabla to try to eliminate problems due to these confounding factors 1 W3 M Mmm 3 Were the conclusions of the study justi ed by the data Answer yes or and explain brie y d The conclusions are not justi ed by the study There are several possible confounding factors that were not adjusted for For example the number of sexual partners is likely to be higher of pillusers than non pill users and it could be that cirvical cancer is a sexually transmitted disease 39 441149me 2 4Mka Please turn over l XzW mm bm quot mw w39 MMM quot W W Question 2 Histograms 8 Points The following three histograms are based on the Old Faithful data set The observations are the duration in minutes for eruptions of the Old Faithful geyser in Yellowstone National Park There exist two types of eruptions shorter ones about 2 minutes and longer ones about 4 minutes Which of the three histograms best describes the underly ing data Shortly explain your answer and indicate why you think the other 2 histograms don t represent the data as well as the one you have selected MMampMW M M quot39a Maw 47110 2137 Mam M 1 mm a Ci 4 Mgww cam was at M M M l h WWW pWMi ao o E p 1 5 25 15 45 55 85 September 13 2002 Your Name Question 1 Measures of Center and Spread 20 Points The table below published in USA Today on Friday May 15 1998 lists the 15 most widely held stocks and their change year to date YTD Suppose we hold one share each of ATampT 65 Bell Atlantic 01 Coca Cola 166 Merck 114 and SEC Comm 34 9 1 Find the average change YTD for the 5 stocks we own Show your work 311 4 4 Stocks included are calms at Menil Lynch 2 Find the median change YTD for the 5 stocks we own mac M n5 01 ill Lit Mg WW 37 mam 1 Statistics 1040 Section 006 Quiz 2 20 Points Show your work 0mg g 03 39 al l66 m s 3q usll KCfal141 IL3V 43V 3 7quot WV 39 I 2 Stock Thurs Chg FlagChg g l 39 5 101 GD amtmwwi 1 H 5wme 1 kwmmuomj m Please turn over 39 3 Find the standard deviation of the changes YTD for the 5 stocks we own giy 1 MMAlM WA r llS 113 6 3 Jim MMAWWJJU 4 1 W M 3 1 3W 2 1 WM 40W 4WM M mg m muomimm 39 ammunxsma e H0336 m ldWljAoM 31x f 24 01 3456 1 ma 23 z 8 SDm ZJTI 81 M avg sum of all numbers how many numbers SD average of deviations from ang 33K 7 3 Statistics 1040 Section 006 Quiz 3 20 Points 1 Sepyember 20 2002 Your Name Question 1 Normal Approximation for Data 20 Points Car drivers in the United States average 12400 miles a year nearly 50 percent more than European drivers The Economist June 22 1996 Assume that the number of yearly miles by US drivers approximately follows a normal curve with a standard deviation of 3200 miles 63 1 Determine the percentage of drivers who travel between 10000 and 15000 miles in a year Wat Q Wadme WWW 3 1 075 111 31M 0481 93am 1 121 1 975 O 090 514 C9 mewwewmw 01 WW mp 4175 05 5167 M 349M Awemeowblsw breath17173 am 9733 3 Mia 7 61233136334466434 EMMWWImM MAM 07800 51677 2733576 W m fun 045 080 1151637 131 Alum vwh 010 27535 64 133ng 561470 W M S ls or aius himn 11401 M smoombk wlgmg 2 And what percentage of drivers travels more than 30000 miles in a year l W 2 35 s a 3 m 121011 30007 Mu 95 42 T116 433441 W n 41mmng 325mm 0 mats 59553943925 107 0501410 44441440106543 mogdm 16g 422 44012 67344360 4133400 we W Show your work Tables Area percent ANORMALTABLE z Area 000 i 0 005 5 399 010 797 015 1192 020 1585 025 1974 030 2358 035 I 2737 040 3108 045 3473 050 3829 055 39 4177 060 E 4515 065 l 4843 070 5161 085 090 095 100 105 1 10 I 15 120 125 130 135 140 145 080 1 57 39 6047 6319 6579 6827 1 7063 7287 7499 39 7699 7887 8064 8230 1 3385 5 8529 l 8664 8789 1 8904 5 9011 9109 9199 9231 1 9357 9426 9438 l 9545 9596 9643 L 9722 7 9756 9786 9812 9836 9857 9876 9892 I 9907 9931 9940 9949 9956 9963 9968 Height Percent z V Area 300 39 99730 310 99806 315 99837 320 99363 325 299885 330 99903 335 3999919 340 99933 345 199944 350 99953 355 99961 360 8 365 99974 370 99973 375 99982 1 380 99986 39 335 99933 390 99990 395 99992 400 999937 3 405 i 999949 i 410 999959 415 39 999967 420 999973 425 1 999979 430 1 999983 39 43539 I 999986 440 999939 999991 445 7 56 5035533 001017 Statistics 1040 Section 006 Quiz 4 2039P0ints Tables September 27 2002 I l Area Height Your Name percent percent Question 1 Percentiles and the Normal Curve 12 Points 39 l 392 1 The Graduate Record Examination GE is a test taken by college students who intend to pursue a graduate degree in the United States For all college seniors and graduates 39 who took the exam in the past few years the mean score for the 39verbal ability portion of A NORMAL TABLE the exam was 497 with a standard deviation of 115 Assuming the scores are bell shaped 1111 in the blanks below Show your work 2 Am z 1 Am 2 Area 1 A student who received a score of 650 on the verbal ability portion of the GRE V 100 quot o 39 L50 8664 300 91730 W 1 exam was at the 51 th percentile of the score distribution 0 05 5 399 L55 3739 3 05 5 997 0194 5 W M 1 33 50 21er 010 797 160 3904 m 99306 44 m 5 4444 Mule 015 1192 165 9011 v 3J5 99337 and 020 1585 1m 65 o 39439 My 15 m3ltm1lampls 5723174 2 1H 170 9109 320 99863 Wm l 025 1974 175 9199 8 MM 0711 135 3230752 1 154 030 2358 130 9281 3330 I K 39 C m 749 1 35 5071 5 4 5114 39 L85 39 335 335 39 99919 39 m 544 9 0 m flow 50 L90 42 340 99933 G 2 A graduate school program igaEii lish will aggt only students with GRE verbal 045 3473 95 9488 345 39 99944 ability scores the top 30 Therefore the lowest GRE score they will a ept is O 395 070 M 55 rr 570 W MMW mvz 132 mm W5 24150738295 trr ass71775 3332 350 99953 4 39 355 1 99961 3079 33 Timhatrme unfo lsr 09m 050 quot5f H37 554 Q60 4515 210 9643 33960 1 99968 I IMF 05 055 u 997 57015 065 4843 215 9684 365 39 99974 2 3907 14 M pmmM 44M 4 xslrr 60 numb A 2 x l 070 I 5161 220 9722 170 99978 Question 2 Correlation 8 Points Fpp 30 C 114139 m i GD 4quotquot I P I it 2 141 am 5 f 075 5467 225 9756 3 75 99982 5 C f 1 080 l 5763 1 If women always married men who were ve years older the correlation betweenlt m 1 085 E 6047 f 139 ng of ahliigbantils and wives would bell l Choose one of the options 9 M5 0 90 61 5 240 9836 390 99990 8 0W7 exp 31 095 6579 mtn 6 a All the points on the scatter diagram would lie on a line sloping up so the 245 9857 395 99992 gt con39elauon would be 1 L00 6827 250 9876 400 999937 39 WMM 39 I gt L05 7063 I GD 2 The correlation between the ages of husbands and wives in the US is 39 L m 7237 39 7 a 43905 993949 NCho ne option and explain b Close to 1 this is like pan 2 with some noise thrown into the data 1 15 74 99 265 9920 1 quot I Comment lnlheMarch I993C IP 1 39 3 me 39 1 39 39 the ages of 39 L l and mg 31 mo EWfo 3021 2332 l L20 7699 23970 9931 43920 993973 4de 27 years older than their wives l 25 78 87 Cr Options a exactly 1 b close to 1 c close to 0 d close to 1 3930 80 j 425 quot 999979 39 t1 1 1 i 430 1 999983 e exac y K E 0 mama 4m 79 144W 285 9956 435 1 999986 3 Elm 75 m 1 mm W mW t 140 g 8385 290 9963 440 999939 I 1 l 1 39WW WW W L 45 V 3529 295 9963 445 39 99399 2 cl 9 5 K 11 I WM 39 3 04 W M 3 w I M Statistics 1040 Section 006 Quiz 5 20 Points October 11 2002 Your Name Question 1 The Regression Line 20 Points In one study the correlation between the educational level of husbands and wives in a certain town was about 050 both averaged 12 years of schooling completed with an SD of 3 years 1 Find the regression equation for predicting the educational level of a wife from the educational level of her husband 10 Points wacr ago 050 W t W avgyod ouugx 2 050l2 W QMM galto 2 Use the regression equation from part 1 to predict the educational level of a woman whose husband has completed IMhooling 5 Points m g J 1 4 W 5 M CmMan m4 Matltme Main Ada77 W M 3 3 Find the rms error for predicting the wife s educational level from t e educational level of her husband 5 Points rMSlnrr Vtwr 51 l 05 3 025 393 1 07g 393 0X 6 3 2SSY 49 v Please turn over ievmw mWAWa mME3 15eugy glgwM 1 y muv M Formulas rms error v1 72 x SDy 3D slope r x SD intercept avgy slope X avgE 2 444me 2 MM WWW 1WW3 X My 3 rWM1m inmazM th 1A4WM Wo KAM 1 443 Mzmwm y mm JAMWWFW 3 M rami W Statistics 1040 Section 006 Quiz 6 20 Points October 18 2002 Your Name Question 1 ChanceProbability 20 Points 1 A deck of 52 cards is shuf ed and two cards are drawn without replacement a 3 Points What is the chance that the rst card is a Q or a 0 M41 wtmusm tmlt Q 39 l M M ls t la 0 39 3 b 4 Points What is the chance that the rst card is a Q and the second card l 126l 00 wwwwwaa lg isaO v 39 I3 UM onqlm o yg MMlsIMWMQMhQ Lquot E E QMMO39M I l Ig f39 flB s Jizag 7 677339 Mls l a 5 SD Fl 24 c 4 Points What is the c3hance that both gr 5 e S J M 1 W M lt m WL te mwm ewlsnlw Mia Minter 7 d 4 Points What is the chance that neither card is a 7 39 35 M lt MM ampW39T memmwi W AmeWIZMIoiW n 39 g i39izg iog97w 5 Eflsl 391 5 10139 h 2 5 Pomts There are two options M il a You toss a coin 100 times on each toss if it lands heads you win 1 if it lands tails you lose 1 on draw 100 times at random with replacement from the box On each draw you are paid in dollars the number on the ticket Which option is hetter Or are they the same Explain brie y 61441 Blwwh Him 23 W WW 39 M Comm WSW8 0 cmx4 WW I u thr 39m in WM Mm man quotan 1 n I F W l yr AW 5 oW 1 1 ram 24 m 13 LIM WIJ 1 4M AWMLWWM ewW 39 ml 1 3u W ml M Whame Wm Statistics 1040 Section 006 Quiz 7 20 Points Question 2 Law of Averages 5 Points OCtOber 25 2002 i The meaning of The probability of a Head is 12 in tossing a coin is best expressed by i saying Your Name 1 The coin has only two sides so the chance of each is 1 2 IV n M ql p39 30 V 2 The coin will come up Heads exactly half the time 50 Heads in 100 tosses 500 Question 1 Box Models EV and SE 15 Points Heads in 1000 tosses and so on A large group of people get together Each one rolls a die 180 times aura counts thine 3 The Odds again a Head are 2 to 1 number Of ones39 Show your work Q he fraction of tosses that come up Head will get ever closer to 12 as more tosses W5 m are made 1 4 Points Find the box model m3 2 Explain your answer Q SK a 1AJWW I mlet wo ia W W4 Jrwb 7 txfrmwMx 2 M MamwszMa w 2 5 Points Find the expected value for the number of ones M 4m MMX 31 1M wwawmlbl qmm tqh 1uzmt xm3 aws141 W 2 3 NLI i Ml lM Wm Formulas Z39NLI sum of all numbers in box how many numbers in box HSU 1 MW 6 5 A143 1ka 39l 3 4111 WM box average box SD average of deviations from box average2 Please tum over EVWquot number of draws x box average 30 39 F i 3 2 I 5 039 Iggy k 039 l SEWquot V number of draws x box SD 525 037217 lam03727 aw 2 1 WW Efraewwa a x In SP I 05031 0lll6 1966 Statistics 1040 Section 006 Quiz 8 20 Points November 1 2002 Your Name Question 1 EV SE and Normal Curve 20 Points According to the US Census Bureau 68 of Utah residents are 18 years of age or older Suppose that 200 Utah residents have been randomly chosen to participate in a survey 1 4 Points Find the box model 2 7 4740 WW 39 0 Mw lg later9 3x 324E xa gfELMWL39 4 IE I 395 Ma W W4W200 Z lraxy maA QlU a 3 179 MMJXA La 4 2 8 Pomts Find the expected number of Utah resrdents 1n th1s sample of 200 who ZiaID S are 18 years of age or older What is the corresponding SE quoti4 W WWaW W EVSM 2w 053 rt 39vq39MCaMRMW l pruXWMA Sew M WW WWW 3 8 Points Using the normal curve nd the chance that at least 130 of the Utah W3 residents in the sample are 18 years of age or older 514 M 2 a3i 49 9 39 36 I data MW 039M 930 6313 Mquot 3 3 le quot a l MQI39W SM am Jquot 03lt9 5070 555 a w Mink 9quot 391 6 1 W 41 Mame 01 W quotW 4 M 15 Max Max 304 M miaLLianJwr the 313m 1 Please turn over Statistics 1040 Section 6 Quiz 9 20 Points November 15 2002 Your Name M 0 My Win 3 cl p37 Question 1 EV SE and Normal Curve 20 Points E M W A group of 50000 tax forms has an average gross income of 37000 with an SD of 20000 Furthermore 20 of the forms have a gross income over 50000 A group of 900 forms is chosen at random for audit Estimate the chance that between 19 and 21 of the forms chosen for audit have gross income over 50000 Show your work A 0 0 A776 1 km W 0717 we 37000 SD 20 0 M 130 MHZ S debJK o r lqwax j qqauorLo W in f P W M 911 WMW 0 3 Mama 00 0090 P N w Liaan W 0 52 0I6 30 1 20 70 ax9 V we Salem TE 100 A AA A K hquot EVgt M300390 Z 370 lZVOa 7 2000 MWM3 353 feet I39M gt301 t2 I2 0 a 62 00 33 SEoo 500 a 0quot re a 0 39 St I I a f A 39 r quot quot3393 quot at 20 21 2100 40 0 7g em 0 076 gm 3394 I W M a7 av 1 Sq 67 x 55 Piease turn over 5quot 1 Statistics 1040 Section 006 Quiz 10 20 Points November 22 2002 Your Name Mr 13WW3 p l2 Question 1 Con dence Intervals 20 Points A real estate of ce wants to make a survey in a certain town which has 50000 households to determine how far the head of household has to commute to work A simple random sample of 1000 households is chosen the occupants are interviewed and it is found that on average the heads of the sample households commuted 87 miles to work the SD of the distances was 90 miles All distances are one way if someone isn t working or is working at home the commute distance is de ned to be 0 Fill the blanks in the statements below and show your work 1 10 Points The average commute distance of all 50000 heads of households in the town is estimated as 7 MA and this estimate is likely to be off by 734w oor so Wiw Marraz m aVZX397 amp WSDWZISD SEMM Amal g grail734 29 l SEouz 92qu ll 2 10 Points If possible nd a 95 c0n dence interval for the average commute distance of all heads of households in the town If this isn t possible explain why a a not 39l 39 41 Mt MM 03 m m we O i m WM m in igkwwm Te Wy wamw Wm Witawe yd w W cam nce WWL 7 23903 X7 039 Please turn over g 9 gw 3MMV 1 we Statistics 1040 Section 006 Quiz 11 20 Points December 2 2002 Your Name W24 WWW p453 Question 1 Tests of Signi cance20 Points Bookstores like education because national data show that 71 of college graduates have read a book in the past year compared to 54 of the general population age 18 and over The data also show the nationwide average educational level to be l years of schooling completed with an SD of about 3 years for persons age 18 and over A bookstore is doing a market survey in a certain county and takes a sample of 1000 people age 18 and over They nd the average educational level to be 1fl years and the SD is 5years Can the difference in average educational level between the sample and the nation be explained by chance variation If not what other explanations can you give Please follow the steps below in answering these questions 1 5 points State the null and the alternative hypothesis for this problem in words and in terms of the box model WWW 0M3 WW MLE lama13 B W W wsWQo Wu Le mav3 1132Ma 2 5 points Calculate the appropriate test statistic WWW3 E mzylluoo395 lsgol E3MMz 1 W 39 WU 13 550 E 11503 03915 55 0J3 I a 3 5 points Obtain the P value use the normal table on the back Mm Pw qudeLIM abw Vf 0 39 3 H1 quot 3j 0 6233 Su 4 5 points State conclusions in terms of rejecting the null hypothesis and in your own words We MWLI Mat 4 W MM 3wa 541 Mare M We 6 4 WM lm 1 was aimHe 2 MM V t l 4M Cam3 quot mu44 1 3 0 a 3 06999 07 n 1 Ma 13 St SD JAM SF CU Z agglgq jnnm W4 3quot Mm AM 259 W W I w m Egyo I W M 4 5 lt w 7quotclawim max7 0014 MM Wl13MMwakm 5 W 4 ML MMw a WMi MWWM l I 2 Statistics1040 Section 006 Quiz 12 20 Points Due on or before December 11 2002 Your Name This is a take home quiz You should work on it on your own and bring it to me on or before the nal examination day Please work on this quiz independently getting as little help as possible from your friends books and notes Question 1 20 Points A thermostat used in an electrical device is to be checked for the accuracy of its design setting of 200 degrees Fahrenheit Ten thermostats were tested to determine their actual setting resulting in the following data 2022 2034 2004 2025 2063 1980 2037 2008 2013 1990 Is the mean setting of these thermometers different from 200 degrees Fahrenheit State the null and the alternative hypothesis calculate test statistic after nding the average and SD of the sample obtain the P value and clearly state your conclusions Assume that the thermometer settings follow the normal curve gld 2Zf1l390 22m 452945 0 dwt39beo6 2022 2m7el f law106742 29 m W 4287 VI3 200 My we was WINquot Ma a P I owl Muse AirM WWW 30min er 9 Li swim SD39 WWMM 591264 1 1 9 se M10741 m C9 SULM 39 g y 2 SE In2 quot3 0 q I 7 2 763902quot rewamm mw mm d 0I5 l 200quot 9 041mm quot4 232 vim n 226 ML 2 ea Ff mm40151 p Willa fa4411 A ltquot nAl laA The following questions are extra credit questions You may obtain a maximum of 20 2 extra points if you complete both questions wmmwwmwam WMWOLWMW Question 2 10 Points In an experiment to stud the dependence of hypertension on smoking habits the following data were taken on 18 individuals db t exp Nonsmokers Moderate Smokers Heavy Smokers Hypertension 21 1 1 36 35 30 13 97 No hypertension 21 I 26 11 21 n 59 i q Is the presence or absence of hypertension independent of smoking habits Conduct an appropriate statistical test to answer this question 7 j 4w 21 Mk ll MMAWMMLeww 1401 CD WW szmhwmw wwlwmm G 11W W ii la txzq Mwyx3 M l 15 ca 1 27 31 3 Question 3 0a Watl f 10 Points A study was made to estimate the difference in salaries of college professors in private and state colleges of North Carolina A random sample of 100 professors in private colleges showed an average 9 month salary of 32000 with a standard deviation of 1300 A random sample of 200 professors in state colleges showed an average salary of 32900 with a standard deviation of 1400 Is there any statistical evidence that professors in state colleges have higher average salaries than professors in private colleges Conduct an appropriate statistical test to answer this question 3971 Lni i t wth awnwarm Cf 2 3339 2 39 T 23948 2 2 quot 272 T Flu Wm Cl Ag f K t 156 CD 27 ll Wax Wiema u3dow 3 442 n3t l Wig MMM 4 WI OW39L 4102 MW 031M swam My W410 39 11W WW 7070M 907 3K J WW3 39 39 wka 34000 M26 39 W 1 3 1 w 39 r g 7 301 g l LOW am Oweans 00 11967 iMxmaomw l wljeim3 m 0 WWquot M W v c ia m5 WM G 2 2 0M3M 06 32300 321120 95 0 WK 0 SamL l00l3000 55463 20041103 mime S B 37 93519 EMA4 39 rod 3930 Emdl 200 a quot SEW Mam 5939 may 0 Z L9 70 99 CD 63 3quot A 039 560 r 0 SS 544 P ngc 2v 0 D i W4 26 CD vb 42 AgJEB MWXM FL MW quot76 D 264 Wm mmw WWW My my mac 0 V M 4354 g Wm M 1 44

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