Statistics Exam 3: Probability and Confidence Intervals, Exams of Statistics

Download Statistics Exam 3: Probability and Confidence Intervals and more Exams Statistics in PDF only on Docsity! Statistics 100 Exam 3 April 7, 2008 0 of 6 pages (11 problems) STATISTICS 100 EXAM 3 Spring 2008 PRINT NAME_____________________________ _____________________ (Last name) (First name) CIRCLE SECTION X1 noon F1 2pm G1 3pm Write answers in appropriate blanks. When no blanks are provided CIRCLE your answers. SHOW WORK when requested. No notes or books are allowed. Calculators (including graphing ones) are allowed. Do not use your own scrap paper. If you need some, ask a proctor. Make sure you have all 6pages (11 problems). DO NOT WRITE BELOW THIS LINE______________________ ____ The numbers written in each blank below indicate how many points you missed on each page. The numbers printed to the right of each blank indicate how many points each page is worth. Page 1 ______19 Page 2 ______17 Page 3______ 29 Page 4 ______20 Page 5______ 15 Score _________ Scores will be posted on Mallard Sunday night and exams will be returned in class on Monday. Statistics 100 Exam 3 April 7, 2008 1 of 6 pages (11 problems) Question 1 (8 pts) Fill in the first blank with the number of draws, and the second with the letter corresponding to the appropriate box model. Choose from the box models below. You may use a box model more than once or not at all. Box A Box B Box C Box D Box E 1 2 3 4 5 6 2 3 4 5 6 7 8 9 10 11 12 1 0 0 0 0 0 0 1 1 -1 a) A die is rolled 100 times and the number of 2's is counted. This corresponds to drawing ______times with replacement from Box ____ b) A pair of dice is rolled twice and the total number of spots is counted. This corresponds to drawing ______times with replacement from Box ____ (Hint: Only ONE of the boxes above is correct.) c) A true/false test has 25 questions. Suppose you guess at random on each question and your scores is computed as the number of right answers minus the number of wrong answers. This corresponds to drawing ______times with replacement from Box ____ d) A coin is tossed 50 times and the number of heads is computed. This corresponds to drawing ___________times with replacement from Box _____ Question 2 (4pts.) A gambler plays roulette 50 times betting $5 on the numbers “13” and “21”. If the ball lands on either “13” or “21” the gambler wins $85, if the ball lands on any of the other 36 numbers the gambler loses $5 a) Which is the appropriate box model? Circle one: i) The box has 34 tickets: 13 marked "85" and 21 marked "-5" ii) The box has 38 tickets: one each of 1, 2, 3, ..., 36, 0, and 00. iii) The box has 38 tickets: 2 marked "85" and 36 marked "-5" iv) The box has 38 tickets: 2 marked "85" and 36 marked "-1" v) The box has 38 tickets: 1 marked "85" and 37 marked "-5" b) How many draws from the box? ___________ Are the draws made with or without replacement? _________ (Fill in first blank with a number and second bland with “with” or “without” Question 3 pertains to the following situation: (7 pts.) A recent Times/CNN telephone Poll asked a random sample of 1004 adults nationwide the following question: “Do you think President Bush should be impeached?” MSNBC posted the same question as a “live vote” where anyone could go to their website and vote “Yes” or “ No”. Here are the results: Yes No Sample Size Times/CNN random poll 33% 67% 1004 MSNBC Live Vote 89% 11% 589175 a) As you can see, the results of the 2 polls are quite different. Which survey gives a better estimate of the percentage of all US adults who would say they think Bush should be impeached? Choose one: i) The MSNBC Live Vote because it has more people ii) The MSNBC Live Vote because people are more likely to answer honestly online than in a telephone interview. iii) Times/CNN survey because the people were randomly drawn. b) Which poll can be translated into a box model? Choose one: i) Times/CNN poll because of random selection ii) The Live Vote because it was online. iii) Both polls iv) Neither poll c) Suppose 100 pollsters each randomly sampled 1000 adults nationwide asking whether they believed Bush should be impeached. All 100 pollsters computed 95% confidence intervals to estimate the percentage of all US adults who believe Bush should be legal. About how many of the 100 confidence intervals would miss the true population percentage? ________________ Fill in the blank. No work is necessary. Statistics 100 Exam 3 April 7, 2008 4 of 6 pages (11 problems) Question 8 (10 pts.) Suppose after the exam tonight I wanted to predict the class average exam score, so I randomly picked 36 exams out of the 900 exams taken to grade. The average of the 36 exams was 80 with a SD of 10. a) Which most closely resembles the relevant box model? Circle one: i) The box has 900 tickets marked with “1”s and “0”s ii) The box has 36 tickets marked with “1”s and “0”s iii) The box has 900 tickets, on each is marked an exam score, the exact average and SD of the box are unknown and but are estimated from the sample.. iv) The box has 900 tickets with an average of 80 and a SD of 10. b) How many draws from the box? ___________ c) The best estimate for the average exam score of all 900 students is ____________. d) What is the SE of the sample average? Show work. Circle answer. e) Maybe I just had bad luck and happened to randomly choose relatively low scores. Maybe the true average of the whole class is really 90 with a SD of 10, If the true average of all 900 students really was 90 with an SD of 10, what is the chance that I’d randomly draw a sample of 36 students and get an average of 80 or less? Choose one: i) Not enough information to calculate since our exam scores don’t generally follow the normal curve. ii) There’s almost no chance of getting an average of 80 or less, since 80 converts to a Z score of about -6 iii) There’s about a 6.5% chance of getting an average 80 or less, since 80 converts to a Z score of about -1.5. Question 9 pertains to the following: (10 pts.) The U of I enrolls about 39,000 students, of whom 26% are graduate students. A simple random sample of 100 students is drawn. a) The EV for the % of the sample that is graduate students is ____ % and the SE for the % is ______% Show work for computing the SE. Round your answer to 2 decimal places. b) This may be translated into a box model by drawing _________tickets ________replacement from which box below? Choose one: (Don’t forget to fill in the blanks above, first one with a number and second one with “with” or “without” i) The box has 39,000 tickets, 26% marked “1” and 74% marked “0” ii) The box has 100 tickets, 26% marked “1” and 74% marked “0” iii) The box has 39,000 tickets marked with “1”s and “0”s. The exact percentages are unknown but are estimated from the sample. c) Suppose 50% of the 38,000 students are female. The SE of the sample % that is female = 5% .Use the normal curve to figure the chance that between 49% and 51% of the sample of 100 is female? Show work and draw a picture. i) Convert the interval 49%-51% to z scores. Note the SE =5%. Show work circle answer. ii) Mark the z scores below on the axis provided and use the normal table to find the appropriate area to shade. Statistics 100 Exam 3 April 7, 2008 5 of 6 pages (11 problems) Question 10 pertains to the 4 boxes and 5 histograms below: (5 pts.) Box1 1 2 12 Box2 99 0 's 1 Box3 1 2 3 4 5 6 Box4 0 1 Histogram A Histogram B Histogram C Histogram D Histogram E Fill in the blanks below to identify the correct histogram. Use each histogram exactly once. a. The histogram for the contents of Box 1 is Histogram_____ b. The histogram for the contents of Box 3 is Histogram_____ c. The probability histogram for the sum of 2 draws from Box 3 is Histogram___. d. The probability histogram for the sum of 100 draws from Box 2 is Histogram___. e. The probability histogram for the sum of 100 draws from Box 4 is Histogram____. Question 11 (8 pts.) A May 2007 Gallup poll asked a simple random sample of 1003 adults aged 18-75 nationwide “Do you think homosexual relations between consenting adults should or should not be legal?” 59% answered “Yes” and 41% answered “No”. a) What most closely resembles the relevant box model? Circle one. i) It has 1003 tickets marked with "0"s and "1"s. ii) It has about millions of tickets marked with "0"s and "1"s, but the exact percentages are unknown and estimated from the sample of 1003 iii) It has about 200 million tickets with numers ranging from 1-10 iv) It has 1003 tickets-59% marked “1” and 41% marked “0” b) 1003 draws are made ___________replacement. Choose one: i) With ii) Without c) What is the SE of the sample percent? (Show work, circle answer.) d) Circle whether each of the statements below is true or false: i) 59% +/- 3.1 is an approximate 95% confidence interval for the percentage of all Americans aged 18-75 who would answer “Yes” to the question above. True False ii) 59% +/- 3.1 is an approximate 95% confidence interval for the percentage of all adults worldwide aged 18- 75 who would answer “Yes” to the question above. True False iii) 59% +/- 3.1 is an approximate 95% confidence interval for the percentage of all Americans college students who would answer “Yes” to the question above. True False iv) 59% +/- 3.1 is an approximate 95% confidence interval for the percentage of all Americans women aged 18- 75 who would “Yes” to the question above. True False Statistics 100 Exam 3 April 7, 2008 6 of 6 pages (11 problems) STANDARD NORMAL TABLE z Height Area z Height Area z Height Area 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 39.89 39.84 39.70 39.45 39.10 38.67 38.14 37.52 36.83 36.05 35.21 34.29 33.32 32.30 31.23 30.11 28.97 27.80 26.61 25.41 24.20 22.99 21.79 20.59 19.42 18.26 17.14 16.04 14.97 13.94 0.00 3.99 7.97 11.92 15.85 19.74 23.58 27.37 31.08 34.73 38.29 41.77 45.15 48.43 51.61 54.67 57.63 60.47 63.19 65.79 68.27 70.63 72.87 74.99 76.99 78.87 80.64 82.30 83.85 85.29 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 12.95 12.00 11.09 10.23 9.40 8.63 7.90 7.21 6.56 5.96 5.40 4.88 4.40 3.96 3.55 3.17 2.83 2.52 2.24 1.98 1.75 1.54 1.36 1.19 1.04 0.91 0.79 0.69 0.60 0.51 86.64 87.89 89.04 90.11 91.09 91.99 92.81 93.57 94.26 94.88 95.45 95.96 96.43 96.84 97.22 97.56 97.86 98.12 98.36 98.57 98.76 98.92 99.07 99.20 99.31 99.40 99.49 99.56 99.63 99.68 3.00 3.05 3.10 3.15 3.20 3.25 3.30 3.35 3.40 3.45 3.50 3.55 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95 4.00 4.05 4.10 4.15 4.20 4.25 4.30 4.35 4.40 4.45 0.443 0.381 0.327 0.279 0.238 0.203 0.172 0.146 0.123 0.104 0.087 0.073 0.061 0.051 0.042 0.035 0.029 0.024 0.020 0.016 0.013 0.011 0.009 0.007 0.006 0.005 0.004 0.003 0.002 0.002 99.730 99.771 99.806 99.837 99.863 99.885 99.903 99.919 99.933 99.9 44 99.953 99.961 99.968 99.974 99.978 99.982 99.986 99.988 99.990 99.992 99.9937 99.9949 99.9959 99.9967 99.9973 99.9979 99.9983 99.9986 99.9989 99.9991 Standard Units -z 0 z Area (percent) Height (percent)