QUE2on Introduction to Statistics in Final Examination | STAT 1222, Exams of Statistics

Download QUE2on Introduction to Statistics in Final Examination | STAT 1222 and more Exams Statistics in PDF only on Docsity! STAT 1222 FALL 2006 Common Final Exam December 8, 2006 PLEASE PRINT THE FOLLOWING INFORMATION: Instructor:__ Student ID:_ - Section/Time: _ THIS EXAM HAS TWO PARTS. PARTI. Consists of 25 multiple choice questions worth a total of 60 points. Read all questions carefully. You may do calculations on the test paper. Mark the number of the opsean sheet corresponding to the test question number with a Number 2 pencil or a mechanical pencil with HB lead. Mark only one answer; otherwise the answer will be counted as incorrect. In case there is more than one answer; mark ihe best answer. Please make sure that your name and [D appear on the opscan sheet in the spaces provided. PART IL. This part consists of 3 problems (40 points in total). You MUST show all the work for each question in the space provided to receive full credit for that question. If you write your explanations in another part of the test, please indicate accordingly. At the end of the examination, you MUST hand in this test booklet, your answer sheet and all scratch paper. FOR DEPARTMENTAL USE ONLY: PART IH Questions 1 2 3 Score Part I Part 1 __ TOTAL STAT 1222 a FINAL EXAM FALL 2006 i. During a race, a sample of five sports cars has a mean speed of 173 mph. The speeds (in miles per hour) of four cars are: 187, 181, 176, 153 Find the speed of the fifth car. a) 165 b) 168 . c) 170d) I71_—e) «178 Use the following information to answer questions 2 and 3. The closing prices (in dollars) of a. sample of six stocks are recorded as: 20 16 15 12 10 3.2 2. The median price of this sample is a) 12> b) 127 ce) 18d) 13.5 e) 15 3. The standard deviation of this sample is a) 2.4] b) 5.28 ¢) 5.79 a) 27.92 e) 33.5 Use the following information to answer questions 4 and 5. ‘The scores on a statistics test. were normally distributed with a mean of 78 and a standard deviation of 7.3. 4. A student who took the test was randomly selected. The probability that he scored between 75 and 95 is closest to a) 6492 b) 3409 ec) 9901 d)-8721_~—se) «312 5. The lowest: test score a student can earn and still be in the top 20% of scorers in the class is closest to a) 80 ob) 82 c) 84 d} 86 e) 87 STAT 1222 FINAL EXAM _PALL 2006 Use the following information to answer questions 14 and 15. The mean cost of renting an apartment in a city is $2000 per month with a standard deviation of $300. Let Z denote the mean cost of rent for a random sample of 60 apartments in this cily. 14. The mean yi, and the standard error og of % are: {a ) jy = 33.33, 0g = 38.73 (b) Mg == 33.38, og = 5 Hy = 2000, a, = 38.73 ig = 2000, oy = 5 Ha = 2000, o% = 300 15. The probability that the sample mean Z is greater than $2050 is: a) .0985 b) .1783 c) .4013 d) 5987 e) 9015 16. Ina survey of 100 adults from the US, 73 were concerned about getling the flu A 90% confidence interval for the population proportion is a) (673, .787) -b) (657, 803) c) (643,817) a) (616, 844) e) (.702, .756) Use the following information to answer questions 17, 18, 19.and 20. A certain restauranl. claims that its hamburgers have a mean fat content Jess than 10 grams. You work for a nutritional health agency and are asked to test this claim. You find that a random sample of 60 hamburgers has a mean fat content of 9.5 grams and a standard deviation of 2.8 grams. 7. Set up the null and alternative hypotheses to test the claim that the mean fat content. is less than 10 grams: a) Api <0, Hy: je > 10 b) Ho: = 13.5, Aa: p< 10 c) Ho: p= 10, Ha: je #% 10 dad) Ho: < 10, Hy: p> 135 e) Ho: 2 10, Hy: p< 10 STAT 1222 FINAL EXAM. FALL 2006 18. The standardized test statistic z is closest. to: a) -02 by) ~18 ce) -1.38 dd) 1.38 e) 18 19, the p-value of this test. is closest. to: a) 0237 b) 0162 ce) 4286. = ed) -S714_—e)- 0838 20. At a= .05, your the decision is: (a) reject Ho and accept H, since the p-value > a (b) fail to reject Hp since the p-value > a (c) reject Hp and accept H, since the p-value < a: (d ( ) fail to reject Ho since the p-value < a e) none of these Use the following information to answer questions 2land 22. A researcher wants to test the hypothesis Hy: p= 0.23 vs Hy: p 0.23. Given that the sample statistics are n = 200 and # = 0.27, 21. The standardized test statistic z is a) -127 b) 127 ec) 188d) 1.34) 1.34 22. At a = 0.1, the researcher's decision is: (a) Fail to reject. Hp because —1.96 < z < 1.96 (b) Reject Hy because z < —1.28 (c} Reject Hp because z > —1.645 (a) ) d (e) Fail to reject Hp because —1.28 < z < 1.28 Fail to reject Hg because —1.645 < z < 1.645 SPAT 1222 FINAL EXAM FALL 2006 23. In a random sample of 19 shoppers at a grocery store, the mean arnount spent was $28.15 and the standard deviation was $12.50. Assuming that the amounts shoppers spend on grocery are normally distributed, construct a 95% confidence interval for the popniation mean amount spent. (a) (22.53, 33.77) (b) (22.18, 34.18) (c) (22.15, 34.15) (d) (26.86, 29.44) ( ) (e) (26.77, 29.53 A real estate agent claims that there is no difference between the mean household Incomes of two neighborhoods. The mean income of 12 randomly selected households from the first neighborhood was Z = 18,250 with a standard deviation of s,; = 1200. In the second neighborhood, 10 randomly selected households had a mean income of Z = 17,500 with a standard deviation s. = 950. Assume normal distributions and equal population Variances, 24. The test statistic is a) -1.536 b) -1232 c) 1.600. d) 1.636 e) 5.437 25. ‘he equation of regression ine between the variables x, and y is given by @ = ~3x + 2,and the correlation coefficient is calculated to be r = ~0.95. Which of the following statement(s) is (are) correct’? I. The variable y is positively correlated to the variable a. Il. The variable y is negatively correlated to the variable « Ill. If ¢ = 5, one would predict that y = 17. IV, If a = 5, one would predict that y = --13. (a) Only Lis true (b) Only IT is true (c) Only 1 and IV are true (d) Only 1 and IV are true (e) Only If and JIE are true STAT 1222 FINAL EXAM FALL 2006 3. The table below shows the Mathematics SATscores for 7 randomly selected students who took the tests twice. Student score on first try score on second try 1 457 532 2 419 523 3 343 427 4 S 539 607 5 394 444 6 413 490 7 392 428 Assume the populations of scores for both times are normally distributed. At a = 0.05, test the claim that the Mathematics SAT scores hnproved on the second try. (a) Hy: Ay: (b) rejection regions (c) test statistics (d) decision (e) interpretation FORMULAS FOR STAT 1222 (Larson and Farber) DESCRIPTIVE: = 2 Sample Mean: = us Sample Standard Deviation s = Lena) L (0 2?) ~ (ay? n n—1l n(n ~ 1) PROBABILITY: P(A or B) = P(A) + P(B) ~ P(A and B) DISCRETE RANDOM VARIABLE: w= SoaP(@) ot =D (c~p)*P(a) Standard deviation: o = Va? . STANDARD SCORE or z~ SCORE: value - mean cmp ™ standard deviation — o CENTRAL LIMIT THEOREM: = ope ge ETH He =H to =F INFERENCE ABOUT POPULATION MEAN (zn): CONDITIONS ¢e- Confidence Interval TEST STATISTIC aT m qt = ' x 3 a o known or n > 30 | $-2,—= << E+ zm z vn Yi is 8 s o unknown, n< 30] F-t.—e < p< E+to~e i= va ~l Va Wi with d.f.=(n—1) with d.f.=(n—- INFERENCE ABOUT POPULATION PROPORTION (p): c- Confidence Interval TEST STATISTIC przafel cp<ptnyf z= tt nm n pq/n MINIMUM SAMPLE SIZE: Zoo to estimate population mean pp: n= ( = ) . . : nn f %o\7 to estimate population proportion p: n= pg (¥) where E is the maximum etror in estimation. INFERENCE ABOUT TWO POPULATION MEANS: CONDITIONS TEST STATISTIC Independent samples, n, > 30;n2 > 30 = (2) = 42) ~ Ga = 2) a4 Mm Ng Independent samples, normal populations ny Or Ng < 30; o?, 72 not equal t= (21 = #2) = (04 = bn) Si 82 oh 4p 2 n ne with df. = smaller of tn, ~ 1) and (nz, — 1) Independent samples, normal populations my Or Ny < 30; of, oF equal t= (Z — Za) ~ (44 — po) (m- Us} +(mg—1)83 [TI mtg -2 Ny Ne with df. =n +tn,—2 Dependent samples, normal populations Ry t t= Ha sa//n CORRELATION AND REGRESSION: Correlation Coefficient: r = t-test for Correlation Coefficient: t = Equation of a Regression Line: § = mz +b ~ m= n> ia? — (S52) Standard Error of estimate: 5, =f Lua)? c-Prediction Interval for y when x = 2% : n(ao — 2)? - < +24 ape © nee hae SY G+ tS. nity ~ (So) Get nyo ty — (S2)Ooy) Vasa (al Vaso with df=n—-2 l-r n-2 bag Ly ~bvy~my zy ME n(xq ~ £)? nt aye —(oaF