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sample - Stat 3011 Spring 2010 Sample Final Exam Stat 3011...

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Unformatted text preview: Stat 3011, Spring 2010 Sample Final Exam Stat 3011: Sample Final Exam Sample Name: keg Instructions From Craig: This is a sample exam that was written by another instructor. The structure of our final exam will be similar to this sample exam. Our exam may include some material we have covered in class that is not on this sample exam. Therefore, this sample exam will be a good place to start studying. but it should not be your only source. The instructions below will also refer to our final exam in Spring 2010: Read each question carefully. The exam is closed book. You may use a calculator and 3 sheets of paper (size 8.5” x 11”) with hand—written formulas or other notes on both sides. No sharing of calculators or formula sheets is allowed. This exam must be your own work entirely. You may not share information with anyone. Any scholastic dishonesty related to this exam will result in an F for the course and a report to the University’s Office of Student Conduct and Academic Integrity. You must provide sufficient details to receive full credit. The Normal, t, X2 and F distribution tables will be attached to the end of the exam. 1/23 Stat 3011, Spring 2010 Sample Final Exam Problem 1 - Multiple Choice and Short Answer Circle one of the listed choices for each question or answer the question directly (no explanati0n is needed). 1. Suppose we are considering students at the University of Minnesota. Suppose 85% of all students own a cell phone, 40% own a car and 5% own neither a car or a cell phone. What is theljprobability that a randomlyllselected student owns both a car and cell phone? 5 (a) .10 Pm = 0‘99” , PM): 0. Ho , INN/16‘) = 0.05 30 ‘- P0403) = PM) +P(6) F paws) (C) .55 s 0.89 4-0-4512 'Cl‘O-C’S’) = 0.3:; Suppose you take 50 measurements on the speed of cars on 1—94, and that the measure— ments follow roughly a Normal distribution. Do you expect the standard deviation of these measurements to be about: . Which of the following is not a statistic: (a) it, the sample mean. (1;) p, the true population proportion. (c) s, the sample standard deviation. . Which of the following is the largest: (a) P(Z > 1) where Z ~ N(0,1). P(t3 > 1) where is ~ t—distribution with 8 degrees of freedom. (c) P(X > 1) Where X ~ N(—1,1). . If you roll two dice simultaneously and add the sum of the dots, which of the f0110wing is least likely? (a) Getting a total of 7. (b) Getting a total of 3. @Getting a total of 12. . Suppose 75% of all students at a large university own a computer. If 4 students are selected independently of each other, the probability that exactly one of them owns a com uter is: p x ~ Binomial 01:4 P: 0.16) o 0.041 —” P(X=1) = Li It; ”(079] (o as)3 :o.oLl-'l 2/23 Stat 3011, Spring 2010 Sample Final Exam 7. 10. 11. If the calculated t statistic is -2.1 for testing H0 : ,u = 3 versus Ha : ,u < 3, based on a sample of size n 2 12, then (a) .01 < P—value < .02 (b) .02 < P—value < .025 @ .025 < P—value < .05 (d) .05 < P—value < .10 PCT” < L196 } :O-O‘IO Pct” <Z.'19l J 2 0-025— . Suppose events A and B are independent, with P(B|A) = .4 and P(A) = .3. Then, 13(3) = _ maxim 5'15? Prev-pm (a) .12 FTBIA) ' mm _" W = 17(5) @ 40 (c) .75 . If we want to estimate a population proportion p with 90% confidence to within :i:0.10 and have no prior guess at the true population proportion. Then, the required sample size is: n _ $047321 (a) 97 — m1 @53 68 : iii—é) (LMCJ‘ (c7. ia)‘ x 616:; ((1)525 Censider two t distributions. One with 5 and on with 9 degrees of freedom. If we calculate the P t > 2. 2) then: P(t5>2.2 >P(tg>2.2) ( ) (b) P(t5>2.2)<P(t9>2.2) (C) P(ts>2.=2) 13059222) Suppose a 95% confidence interval based on a sample of size 100 for a populati0n proportion p is (.05, .12). The correct interpretation of this interval is: (a) there is a 95% chance that p falls within the interval (.05, .12). @ if 95% confidence intervals were calculated for all possible samples of size 100, 95% of these intervals would actually contain p. (c) for 95% of all possible samples of size 100, the population proportion p would fall within the interval (.05, .12). 3/23 Stat 3011, Spring 2010 Sample Final Exam 12. Which of the following is not a requirement for a binomial distribution? There are a fixed number, n, of observations. (b) The n observations are independent. (0) The proportion of success for each observation, p, is between 0 and 1. (d) There are only two possible outcomes. 13. The twouway table below describes demographics of US. households: Owns cell Does not own phone cell phone Has Internet access Does not have Internet access Suppose we randomly select a US. household. The events “household owns a cell phone” and “household has Internet access” are independent. (b) are not independent. (c) may or may not be independent — there is no way to tell from the given informa- tion. 14. Suppose Z N N(0,1), then the 2* value such that P(Z > 2*) : 0.03 is (a) 2.17 @ 1.88 P( €71.88) -= 0.46% 15. Which of the following statements is not true about normal curves? Every normal curve is symmetric about 0. (b) Every normal curve is bell—shaped. (c) Every normal curve is centered at its mean. 16. If we fail to reject H0 when HA is really true, then (a) we have committed a Type I error. we have committed a Type II error. (c) we have not committed any statistical error. 4/23 Stat 3011, Spring 2010 Sample Final Exam 17. 18. 19. 20. 21. For Problems 17 - 21 we wish to compare two HIV drugs for reducing the level of HIV virus circulating in the blood of HIV positive patients. 20 patients are given drug A and 20 patients are given drug B. The sample mean decrease and sample standard deviation in level of HIV for each drug after two months is as follows: TLAI27 Lil/1:138 SA=0.42 71.3223 373320.95 53:0.28 Which of the following describes the above setting. .lTwo—sample t inference. (b) Two—sample proportion inference. (c) Matched pairs t inference. Suppose we are interested in if there is evidence that drug A out—performs drug B, then appropriate alternative hypothesis is: (3.) HA ZMA?£HB .HAiMA>.UB (0) HA iMA <lu’B Suppose you calculate a 95% and 90% confidence interval for the difference in true means, “A — ,uB based on the same sample. Which of the following must be true. (a) The 95% confidence interval is the same length as the 90% confidence interval. ® The 95% confidence interval is longer than the 90% confidence interval. (0) The 95% confidence interval is shorter than the 90% confidence interval. What is the appropriate t-critical value for a one—sided o: = 0.05 level test? (a) 1.645 (b) 1 706 (:) 1 717 _::: Eéi'maq (d) 2.052 "”‘ *1: (e) 2.074 The conclusion of a one-sided a = 0.05 level test should be: ReJect Ho. 1:: 2‘ _E3 ”8 _ 0.4: (b) Reject HA. u a : M = 43:9 . . EB.— +-g_'5. 0-4-2" 0.281 (0) Fall to reject HO. on ne 7:: -+ 23 (d) Fail to reject HA. 5/23 Stat 3011, Spring 2010 Sample Final Exam 22. 23. 24. For Problems 22 and 23, the following is part of the R output for the regression of BAC (Blood Alcohol Content) on Beers (the number of beers drank). Call: lm(formula = BAC " Beers) Coefficients: Estimate Std. Error 1: value Pr(>|t|) (Intercept) -0.012701 0.012638 -l.005 0.332 Beers 0.017964 0.002402 7.480 2.97e-06 Residual standard error: 0.02044 on 14 degrees of freedom Multiple R‘Squared: 0.7998,Adjusted R—squared: 0.7855 F—statistic: 55.94 on 1 and 14 DF, p-value: 2.969e-06 Is there significant evidence that the number of beers impacts BAC? To answer this question, we need to test the hypotheses (a) H0:fi=0versusHa:,3>0. .H0;s:0versusHazs¢e. (c) H0:a=0versusHa:cr>0. (d) Haza:0versusHa:a7£0. From the above test and the regression output, we should conclude: There is significant evidence that the number of beers impacts BAC. (b) There is significant evidence that the number of beers does not impact BAC. (c) There is not significant evidence that the number of beers impacts BAC. A large real estate firm wants to use regression analysis to estimate the market value of their properties. Each of the following three models were fit to data collected from a random sample of 20 properties: Model 1: y I a + film Model 2: y = a + 01331 + 152592 Model 3: y 2 a + BxI1+ [12:62 + 163533 where y = sale price of the property, I; : size of property, 5122 = distance to the nearest Starbucks, and :53 I number of cats owned by the most recent owners. Which model has the largest R2? (a) Model 1 )Model 2 @ Model 3 (d) This cannot be determined without analyzing the data. 6/23 Stat 3011, Spring 2010 Sample Final Exam 25. 26. The following 6 problems refer to the situation described below: Researchers interested in predicting marijuana abuse among high school students col- lected data from a random sample of 89 high school students. The students rated their marijuana use on a scale from 1 (non-user) to 4 (frequent user}. A multiple regression analysis used grade point average (GPA), a popularity score, and a depression score to predict marijuana use. The true linear regression model can be written as y=a+fifl1+fi2$2+53$3+5 where y : marijuana use 3:1 : GPA $2 = Popularity :53 2 Depression Consider the following results obtained from R: Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.393 0.0914 4.30 <2e-16 GPA —0.597 0.1312 -4.55 <2e-12 Popularity 0.340 0.1264 2.69 <2e~12 Depression 0.030 0.0112 2.68 <2e-12 Multiple R-Squared: 0.3412, Adjusted R—squared: 0.3148 F—statistic: 14.83 on 3 and 85 DF, p-value: < 2.2e-16 What is the best interpretation of the test H0 : {5’1 2 0 versus Ha : 61 7i 0? (Mark your choice) (a) H0: GPA is not a good predictor of a. student’s level of marijuana use H0: when we already know popularity and depression scores for a student, GPA does not add a significant amount of predictive information about a student’s level of marijuana use What is the predicted marijuana use score for a student with a GPA of 2.0, a popularity score of 3.1, and a depression score of 2.3? C)(nnz Q: aaqa — acqrczei-+ 0340(aJ)-ro.os(za) (b) 0.341 : a. 322 (c) 0393 (d) 2467 7/23 Stat 3011, Spring 2010 Sample Final Exam 27. Which of the following is a proper interpretation for 31, the estimated regression coef- ficient for GPA? (a) A student with a GPA of 2.0 will have a predicted marijuana use score of -1.194 (b) If we take 10 students with GPA‘s of 2.0 and 10 students with GPA’s of 3.0, we expect the difference in these groups’ average marijuana use score to be 0.597. @ At any fixed level of popularity and depression, an increase of one point in GPA is associated with an estimated 0.597 point decrease in marijuana usage. (d) .01 is negative, so we can assume that GPA and marijuana use are negatively correlated. 28. Approximately what percentage of the variability in marijuana use scores is explained by its relationship with GPA, popularity and depression? (d) 96.796 29. Based on only the F statistic in the output, we would reject Hg for the F test and conclude: At least one of GPA, popularity or depression is linearly associated with marijuana usage. (b) GPA, popularity and depression are all linearly associated with marijuana usage. (c) None of GPA, popularity or depression are significantly associated with marijuana usage. (d) There is a curved relationship between marijuana usage and at least one of GPA, popularity or depression. {H9361 ={52‘=(3r4 =0 H“; P” [fag-t one parameter- is flat 63mm 1b 0. 8/23 Stat 3011, Spring 2010 Sample Final Exam The following 4 problems refer to the situation described below: At what age do babies learn to crawl? Does it take longer in the winter, when babies are often bundled in clothes that restrict their movement? In order to study the possible affect of birth month on the age at which babies learn to crawl, data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported the birth month and the age (in weeks) at which their Child was first able to creep or crawl a distance of four feet within one minute. The resulting data were grouped by month of birth. The data are for January, May, and September. Some summary statistics for the age at which babies learn to crawl are given in the following table: Month of birth January 31.03 0.995 32 May 29.54 0.998 27 September 34.76 1.190 38 30. What are the response variable and factor in this experiment? Pegponge 2 Age in Week; 611- which child Was firm: able +0 Creep or Crawl a dismance 0F 4 Feet in CI. mu‘nure Fat-far 2 Harri-M 0? bir-fh 9/23 Stat 3011, Spring 2010 Sample Final Exam The following is the ANOVA table for this data, with some numbers omitted: —I—-- Ms month XXXXX 241 ZZZZZ <25e-16 31. The number that should go in place of XXXXX is .2 e— da = 6H (b) 3 (c) 94 (d) 95 32. The number that should go in place of YYYYY is (a) 2 @94 e— da -; Nag 33. The number that should go in place of ZZZZZ is (a) 3.89 (b) 32.08 (c) 87.72 .182.58 P: Between 15mm vavrabI'mq wz-mrn Paroups vavfabnflq : 7—44 1.32 '= [92.916 10/23 Stat 3011, Spring 2010 Sample Final Exam Problem 2 Let a: : the service hours on a particular outboard boat motor at failure. Suppose that the distribution of a: is well approximated by a normal distribution with mean 2,000 hours and standard deviation 300 hours. (a) Suppose the manufacturer’s warranty covers the motor up to 1200 hours. What is the probability the motor will fail within the warranty time? X. "’ N(ZOOO, J00) X’ZOUU {loadzood . X .: Pt (1200) P mm < a“ ) P ( 33 <: ——2.e'1) -= 0.0032 (b) What is the value 22* such that only 6% of all motors last for a longer time than this value? :9 :: 7:: - 0.05 X ”“0090. 30c) A 0 gr «3"“0-0 = 7,000 4- (L69)(3ov’ = 24-69 11/23 Stat 3011, Spring 2010 Sample Final Exam Problem 3 Suppose that the professional sports team preferences of U of MN students are as follows: was: 62% like the Vikings :9 V 3 pcv) = 0-6?- 35% like the Twins (gilt ”I" # PC” = OJ); 19% like both the Vikings and the Twins :3 P(V n-r) :- 9, ,q Suppose we select a U of MN student at random. (51) What is the probability that the student chosen likes the Viking or Twins (or both)? [’(VUT) = Pcw +P(T) rprvm') = 0.62 + 0.35- -— 0J4 = 0.18 (b) What is the probability that the student chosen likes the Vikings but does n_ot like the Twins? PWan-i = Pw} —P(vnT) = 0.62— OJQ : O-H-B (0) Are the events “likes the Vikings” and “likes the Twins” disjoint? Why or why not? Theq are not di'Sjoiflt fince Pcvn‘ri ¢Q 12/23 Stat 3011, Spring 2010 Sample Final Exam Problem 4 The Montana Highway Patrol is interested in determining whether Montana residents or nonresidents drive faster on a particular stretch of Interstate 90. Independent random samples of the speeds of cars having Montana license plates and cars licensed in others states resulted in the below summary data (assume both samples are from populations with approximately normally distributed speeds): License plate Sample Size Sample mean _—I | 29 _— Let in = true mean speed driven by residents of Montana on 1-90 and m = true mean speed driven by nonresidents on 1-90. (a) Calculate a 90% confidence interval for the true mean speed driven by residents of Montana on 1-90. __ g: XI :13 ta.o§.d-F=ZI; m = ”(as :t (1.103) { 32;) = 16.4 “1‘ Law? .— -'_ (114.46, 78-34) (b) Interpret your confidence interval in the context of the problem We Can be Q0 ”/a Confident that The me mean gpeed driven b3 Yesrdenfg OF Hortfano. or! 1.430 .7, 19mm ”tr—Lure mph and 19.34 mph. 13/23 Stat 3011, Spring 2010 Sample Final Exam Problem 4 continued (c) Is there significant evidence that the mean speeds of Montana residents and nonres— idents on 1—90 differ? Test at level of significance or = .05. Remember to state the appropriate hypotheses, calculate the test statistic, calculate a P-value (or use critical value), and give yOur conclusions in context of the problem. quo-meses Ho “17“: V5 Ho: “(1112. T251“ 935911; 1-— ”Z ~73; 16.4»133 ‘3 -—-——-___._ 2 _- .53.: ’31 as” 9.9; [‘24 flu r]; 7—6 +—_ZQ P—value _____ 4.24 LZQ P—value ~— 2x PCB; <‘-—I.24-) 7 0.2. Conclusr‘on A“? -H‘Ie 0.0: anificance level, we cannot reject H». We do ”of have enough ewdeme. ‘l'o Con dude +hod: he mean greed; cue Honma recidem‘s and non Midmg on I-Qo drFFev, 14/23 Stat 3011, Spring 2010 Sample Final Exam Problem 5 An airline’s public relations department says that the airline rarely loses pas- sengers’ luggage. It further claims that on those occasions when luggage is lost, 90% is recovered and delivered to its owner within 24 hours. A consumer group who surveyed a large number of air travelers found that only 104 of 123 people who lost luggage on that airline were reunited with the missing items by the next day. (a) State and verify the 3 necessary assumptions for calculating a 95% confidence interval for the population proportion, p. l: reunited wan luggage next dag 1._ C‘afegomal vawame M manned w'rH’l luggage new dag 2. Pandanimon 3. Expeaed number; 0? §uccesses and fimures 7/!‘5 [- n3: 123- 1:: :qu 7115 "(I‘?J ‘5 [2% (I- :2"; _—_ ‘q 7;“,- (b) Calculate a 95% confidence interval for the true proportion luggage returned within 24 hours. A A h + f P C l—P) " = l° q. : P —- n where P '23 0.846 = 0.3% ‘3 Lab ia-WGU-O-mi I29 7- 0.946 1". 0.064- (0.1 5’2. , 0.406;) 15/23 Stat 3011, Spring 2010 Sample Final Exam Problem 5 continued (c) Does the survey provide sufficient evidence that truth is less than the airlines claim? Test at a = .05. (i) State appropriate hypotheses. (ii) calculate the test statistic1 (iii) calculate a Puvalue {or use critical value), and (iv) give your conclusions in context of the problem. (i) qumeses 'Ha: 19:99 vs Ha: P<o.q GU Ties-r fiumrrc 2: LL _ 0-946 we I——- ' ‘—'—'-—-—— : -2, paCf’PI) jo_4(r,o'q’ 0‘ n :22. (iii) P - vauue __,_._._-—--' «2.0 I P—Vame = P(-‘2 (rarer) = 0.07.2.7. (iii) Gnclusron _________. At fine 0.0:; Q‘qnifi‘cance level, we (an rent fine nutl hlojpafflegr‘§_ We have evideme Heat ~rhe me pwpar+ron a? lofi: luggage float is remarried wamn up hours is less Hum +he airtmes ctarm. 16/23 Stat 3011, Spring 2010 Sample Final Exam Problem 6 Does gasoline type effect miles per gallon (MPG) in automobiles? 24 cars were randomly selected from a large study group. 12 cars were chosen at random and run first with regular gas, then with premium gas and the MPG was measured for each. The other 12 cars were given premium gas, and then regular gas and the the MPG was measured. The following are the summary statistics from the experiment. (assume both samples are from populations with approximately normally distributed MPG’S) Difference (Reg - Pre) -18 (a) Do we have Two—independent samples? Why or why not? Circle: YES or @ ‘The ”PG 0F 0 (m- ucmg gas is flat Independent 0? we Hpcq 01C +haf Same Car using plasmium gar, (b) Is this a matched pairs design? Why or why not? Circle: @ or NO ‘me we samples ure fhe some subjects (Cfll'f)_ (c) Is there significant evidence, at a = .01, that the use of premium gas increases MPG? (i) State appropriate hypotheses, (ii) calculate the test statistic, (iii) calculate a P—value (or use critical value), and (iv) give your conclusions in context of the problem. (3 J quomeses Ho:}4‘.d=0 V5 Ha: place UT) T696 W ‘t= E— : i... = -2.et; cal/m 9'37sz (iii) P—umue : : P'Value = P(’cz; < ,1“) (0.0. —2.65 (W) Conclusro n At we om S‘iqn'rfi'caflce level. we Can vejert fine ”‘4" “WWW“. We have Evidence fiat we age «9 prawn: gag increases MPéx. 17/23 Stat 3011, Spring 2010 Sample Final Exam Problem 7 The following is R output from a linear regression of poverty rate on high school graduation rate for the 50 states. (NOTE: A state in which 10% of the residents are living below the poverty line has a poverty rate of 10%. Similarly, a state in which 90% of residents graduate from high school has a high school graduation of 90%.) > fit <- lm(poverty"HighSchool)...
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