MAT221-2002Fall - MAT 2‘21 NAM-EL LH'BEV “an Signature...

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Unformatted text preview: MAT 2‘21 NAM-EL LH'BEV' “an: Signature: Instructions: Final Exam Dec. 16, 2002 You should have 12 pages (6 sheets) 11 problems. C1 Write the answers and show the main steps of your work on this test sheet. Your final answers must include the appropriate units (eg. dollars, dollars per week, miles per hour, etc.) If you use a table, state the table used: for example, 1.887 (from Table W). if you use a function on the T183 (or T189) write out the command you entered as well as the result: ‘ for example, 0.0668 (normalcdf(-10,-1.5,0,1)). DO NOT WRITE ON THE REST OF THIS COVER SHEET! (Your instructor will use this sheet for recording your scores.) Problem 105) Problem 4(4) Problem 2(15) Problem 5(11) Problem 3(4) Problem 6(10) Problem 7(8) PART 1(34) PART 2(33) Problem 8(8) Problem 9(4) Problem 10(11) Problem 1100) PART 3(33) Totaluoo) 2 MAT 221 Final Exam A] PART 1: Chapters 1 & 2 Problem 1 (15 points) Consider the 25 test scores (based on 100 points) in the following stem plot: GOA \101 2357 i—ANJOOnD-CHOEKIOO HQNJOJHMO Lowcvoows a. (5 points) Give the five-number summary of these scores b. (3 points) List any suspected outliers using the 1.5 x IQR rule. If you think that there are none, say so. c. (3 points) With no further computations you should be able to decide which of the following six statements about these scores are valid and which are not valid. Circle all valid statements. the data is unimodal the data is bimodal the data is approximately normal the data is not normal mean > median median > mean d. (4 points) The instructor feels that the test was too long for the time period and decides to curve the scores using the linear transformation y = 44 + g2: This will make the top score 100 and bring the minimum score up to just above 50. (i) The median of the curved test scores is (ii) The standard deviation of the original scores was 19.4; the stan- dard deviation of curved test scores is MAT 221 Final Exam A1 3 Problem 2 (15 points) The following data on birth weights (tn pounds) of twins is taken from the Indiana Twin Study: Observation # l 2 3. 4 5 6 7 8 9 10 thn1 (ct—data) 4.1 4.6 4.8 5.2 5.3 5.5 5.6 5.9 5.9 6.3 thn2 (y—data) 6.3 4.3 4.6 5.8 5.4 5.4 6.2 5.7 4.8 6.1 a, (5 points) Make a scatter plot of the data: y-axis 4.0 4.5 5.0 5.5 6.0 6.5 b. (4 points) Given the following information, 2551‘: 53.2, 2:512 2 287.06, inyl- = 29127, ,ay 2 5.46, sy = .696, compute to 3 decimal places: (i) the x-data mean, pr = _; (ii) the :r—data standard deviation 81 = ; c. (4 points) The correlation coefficient r is 0.19. Circle the equation of the linear regression line for predicting y from :13: y:6.5—.2a:, y:4.4+.21:, y=:1:, y=4.9+.19x, y=6—.19r. d. (2 points) Using this regression line, predict the birth weight of the second twin if the first twin weighs 6 pounds: 4 MA T 221 Final Exam Al Problem 3 (4 points) Suppose that the readings of a certain blood test are normally distributed with mean 17 and standard deviation 3 'we have pictured this distribution below. a. (2 points) Compute the z-score of a test result of 15.2. b. (2 points) Roughly what percent of the test readings are greater than 20? How did you get this? M AT 221 F inal Exam A} 5 PART 2: Chapters 3 8c 4 Problem 4 (4 points) A researcher is interested in the possibility that extra vitamin C will decrease the number of colds a person would catch over the course of one year. He plans a year long study involving 1,200 adults and doses of 0, 1,000 or 2000 units of vitamin C. a. {I point) Who are the subjects? I). (I point) List the factors or explanatory uariable(s): c. (I point) List the treatment{s): d. (I point) List the response variablels): 6 MAT 221 Final Exam A1 Problem 5 (11 points) The event, C, that a US. hospital birth is a C- section has probability 0.125; P(C = 0125). Let M be the event that the mother in a US. hospital birth is a member of a minority; assume that P(M) = 0.32 and P(C and M) = 0.03. a. (2 point) What is the probability that a randomly selected U. 5'. hospital birth is not a C—section? [Show your work] b. (2 point) What is the probability that 3 randomly selected U.S. hospital births will not include a C—section? [Show your work] 0. (2 point) Compute: P(C or M) 2 [Show computations] d. {2 point) Compute: P(C|l\/I) : [Show computations] e. (3 points] Complete the following Venn diagram by filling the probabil— ities in each of the four separate areas. 0 C MAT 221 Final Exam A1 7 Problem 6 (10 points) Peter selects one card from a standard deck of 52 cards. If he selects a face card (jack, queen or king), he wins $4; if he selects any other card except an ace, he wins $1; however, if he selects an ace, he must pay $20. Let the random. variable X be the winnings on a single draw. a. (2 points) Fill the probabilities in the following table. You may keep them as fractions or compute them to three decimal places. X —20 1 4 p b. Compute: (i) (2 points] MX = [Show computations]. (ii) (2 points) ox = [Show computations]. c. The game is extended to include a second part: a second card is selected and if the two cards form a pair (2 aces, 2fiues, etc.) Peter wins $16 otherwise he must pay $1. If we let the random variable Y be the winnings of this second step, Y 16 #1 and uy = 0 while 0y = 4. P '17 1-7 (W. Then the rando 2a 6 of the winnings of the combined game is Z = X + Y. ompute: (i) {2 points) p2 = [Show computations]. (ii) (2 points) 02 = [Show computations]. Nab. X“! WM 8 MAT 221 Final Exam Al Problem 7 (8 points) A postalfacility has two letter sorting machines. Ma- chine A handles 60% of the sorting and machine B sorts the rest. Machine A misreads the zip code with probability .005 while machine B misreads the zip code with probability {015. a. {4 points) Construct a tree diagram for a randomly selected letter (which machine processed it and whether its zip code was read correctly) and label the branches of the tree with appropriate probabilities. b. (2 points) What is the probability that a letter’s zip code will be misread? c. (2 points) Ifa letter’s zip code is misread, what is the probability it was processed by machine B? MAT 221 Final Exam A1 9 PART 3: Chapters 5 & 6 Problem 8 (8 points) A biased coin comes up heads 45% of the time. a. (2 points) What is the probability that, in flipping this coin 10 times independently, you will have exactly 1 head? b. (4 points) Compute the mean and standard deviation for the binomial distribution of the number of heads in 10 flips of this coin: c. (2 points) Use the normal approximation with the continuity correction. to estimate the probability that in 10flips there will be 3 or fewer heads. [Show the z-score you use or your calculator entry] 10 MAT 221 Final Exam A1 Problem 9 (4 points) In each case, state the null hypothesis and the alter- native hypothesis. a. (2 points) Last year, your company "3 service technicians took an average of 2.6 hours to respond to trouble calls from business customers who had purchased service contracts. Does this year’s data show a diflerent response time? b. (2 points) Larry ’3 car averages 32mpg on the highway. He now switches to a new motor oil. After driving 3000 highway miles with the new oil, he wants to know if his gas mileage has increased. MAT 221 Final Exam A1 11 Problem 10 (11 points) The mean and standard deviation of the Survey of Study Habits Ed Attitudes test (SSH/1) for US college students are 115 and 30, respectively and the test scores are normally distributed. A teacher wonders if the students at his university would score diflerently on this test. He gives the test to a random sample of 60 students at his school. The mean for this sample is T = 104.3. We denote the mean of the scores of all students at his school by ,u and assume that the standard deviation would be the same as for the entire population, a = 30. We take H0: '11 = 115 Ha: 11 3A 115 a. (3 points) Find the value of the z-statistic. b. (3 points) Compute the P-value. c. (2 points) Is this statistically significant (circle your answers) at the 5% level? Yes No at the 1% level? Yes No d. (3 points) What would the P-value be if he only wished to test if the mean of the student ’5 test scores at his school was less than 115? 12 MAT 221 Final Exam Al Problem 11 {10 points) A test for the level of potassium in the blood is not perfect. Moreover the actual level of potassium in a person’s blood varies slightly from day to day. Suppose that repeated measurements for the same person on difi’erent days are independent and vary normally with a standard deviation of 0.19. a. (3 points) Jane’s potassium level is measured once. The result is :c = 3.2. Give a 95% confidence interval for her mean potassium level. [Show your work! / b. (3 points) If measurements are taken every day for a week and the mean result is T = 3.24, give the 95% confidence interval for Jane’s mean blood potassium level? [Show your work!/ cs'llnu'h c. (4 points) How many measurements must Jane take to compete her blood potassium level within i0.1 with 95% confidence? ...
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