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 November 16, 2004 STATISTICS 100 EXAM 3 FALL 2004 PRINT NAME_____________________________ _____________________ (Last name) (First name) CIRCLE SECTION M1 9am C1 noon S1 2:30 pm 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 7 pages (15 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 2 _____ 18 Page 3 ______24 Page 4______14 Page 5______ 20 Page 6 ______ 24 Total Score _________ Exams will be returned in class on Thursday. We’ll be starting Chapter 26 which covers very important material so be sure to come!! 1 of 7 pages (12 problems) Statistics 100 Exam 3 November 16, 2004 Question 1 (4 pts.) For the following questions circle the more likely possibility. If they’re equally likely circle both: a. (i) Playing roulette 400 times, betting $1 on red each time and coming out ahead (ii) Playing roulette 25 times, betting $1 on red each time and coming out ahead. b. (i) Tossing a fair coin 1000 times and getting exactly 50% heads. (ii) Tossing a fair coin 10 times and getting exactly 50% heads. c. (i) Tossing a fair coin 100 times and getting between 40% and 60% heads (ii) Tossing a fair coin 400 times and getting between 45% and 55% heads d. (i) Tossing a fair coin 100 times and getting less than 40% heads, (ii) Tossing a fair coin 1000 times and less than 40% heads.` Question 2 (14 pts.) Fill in the first blank with the number of draws and the second blank with the word "with" or "without", then circle the appropriate box model. a) A gambler plays roulette 100 times betting a $1 on the number “7” and “11” each time. If the ball lands on “7” or “11” he wins $17, if it lands on any other number he loses $1. There are 38 numbers: 0,00,1,2,3,…,36. This corresponds to taking the sum of ________draws ____________replacement from which of the following box models? i) The box has 100 tickets, 2 marked "17" and 98 marked "-1" ii) The box has 38 tickets: one each of 1, 2, 3, ..., 36, 0, and 00. iii) The box has 38 tickets, one marked “7”, one marked “11” and the rest marked “0”. iv) The box has 38 tickets, 1 marked "35" and 37 marked "-1" v) The box has 38 tickets, 2 marked "17" and 36 marked "-1" b) A multiple-choice test has 25 questions. Each question has 5 possible answers, only 1 of which is correct. Each correct answer is worth 4 pts. and 1 pt is deducted for each incorrect answer. Suppose you guess at random on all 25 questions and your score is computed. This corresponds to taking the sum of ________draws____________ replacement from which of the following box models? i) The box has 25 tickets, five tickets are marked “1” and twenty are marked “0”. ii) The box has 5 tickets, one marked "1" and four marked "0" iii) The box has 5 tickets, one marked "4", and four marked "-1/4". iv) The box has 5 tickets, one marked "4", and four marked "-1". v) The box has 25 tickets, one marked "4", and the rest marked “-1”. c) You roll a die 30 times and count the number of “2”s. This corresponds to taking the sum of ________draws ____________replacement from which of the following box models? i) The box has 6 tickets, 1 marked “1” and 5 marked “0”. ii) The box has 6 tickets, 1 marked “2” and 5 marked “0”. iii) The box has 6 tickets: one each of 1,2,3,4,5,6. iv) The box has 30 tickets: 5 each of 1,2,3,4,5,6. d) A fair nickel and a fair dime are each tossed once and the number of heads is counted. This corresponds to which of the following 3 options? Option 1: One draw from a box containing 3 tickets: one marked “0”, one marked “1” and one marked “2” . Option 2: Two draws with replacement from a box containing 2 tickets: one marked “0” and one marked “1”. Option 3. One draw from a box containing 4 tickets: one marked “0”, two marked “1”, and 1 marked “2”. Which is the correct option(s)? Circle only one. i) Only Option 1 iv) Option 1 and 2 are correct. Option 3 is not. ii) Only Option 2 v) Option 2 and 3 are correct. Option 1 is not 2 of 7 pages (12 problems) Statistics 100 Exam 3 November 16, 2004 Question 8 (2 pts.) A poll is taken in a city of population 100,000. A simple random sample of 1,000 is chosen and polled. Another poll is to be taken in the same way from a city with a population 100 times bigger (10 million people). In order to obtain the same accuracy as in the first city, the sample size in the second city should be: i) 100,000 ii) 10,000 iii) 1,000 iv) 100 Question 9 (6 pts.) A Fox News Poll asked a random sample of 900 adults nationwide the following question: “Do you personally believe in the existence of the Devil?” 71% of the people in the sample answered “YES”. a) The SE of the % of people in the sample who said “YES” is about 1.5%. An approximate 95% confidence interval for the percentage of all American adults who believe in the Devil is: i) (66%-76%) ii) (68%-74%) iii) (69.5%-72.5%) iv) (70.85%-71.15%) b) If the researcher decreased the sample size to only 100 people, the length of the 95% confidence interval would i) be multiplied by 3 ii) be multiplied by 9 iii) be divided by 3 iv) be divided by 9 v) be multiplied by 81 c) In the same poll of 900 people, 92% answered “Yes” to the question:: “Do you personally believe in the existence of God?” Would the SE of the % of people in the sample who said “YES” to this question still be 1.5% as in question (a)? i) Yes, it would be exactly the same ii) No, it would be bigger iii) No, it would be smaller Question 10 pertains to the following situation: (12 pts.) A Harris Poll asked a random sample of 1,000 adults nationwide the following question: “Are you very afraid of mice?” 10% of the people in the sample answered “Yes”. a) What most closely resembles the relevant box model? Circle one. i) It has 1,000 tickets, 10% marked "1"and 90% marked"0". ii) It has millions of tickets, with an average of 0.10, but the SD is unknown. iii) It has millions of tickets marked with "0"s and "1"s. The exact percentages are unknown but are estimated from the sample. iv) It has millions of tickets, 10% marked "1"and 90% marked"0". b) The draws are made ___________replacement. i) With ii) Without c) What is the expected value for the percent of all US adults who are very afraid of mice?__________% d) What is the expected value for the percent of all US women who are very afraid of mice? i) 90% ii) 10% iii) not enough information to determine e) Calculate the SE for the percentage of people in the sample who answered "YES". Show work, circle answer. (Round to 2 decimal places.) f) Suppose the poll was taken just in Chicago (instead of nationwide), how should the pollsters adjust the sample size to keep the same SE? 5 of 7 pages (12 problems) Statistics 100 Exam 3 November 16, 2004 i) Significantly increase sample size ii) Significantly decrease sample size iii) Keep sample size about the same 6 of 7 pages (12 problems) Statistics 100 Exam 3 November 16, 2004 Question 11 (14 pts.) A health survey asked a random sample of 1600 college students nationwide the following question: “How many alcoholic drinks have you consumed in the past 2 weeks?” The sample average was 20 drinks and the SD was 16. a) What most closely resembles the relevant box model? Circle one. i) It has 1600 tickets marked with "0"s and "1"s. ii) It has millions of tickets marked with "0"s and "1"s, but the exact percentage of each is unknown. iii) It has millions of tickets. On each ticket is written a number indicating the number of drinks. The exact average and SD are unknown but are estimated from the sample. iv) It has 1600 tickets. The average of the tickets is 20 and the SD is 16 b) The draws are made ___________replacement. i) With ii) Without c) What is the SE of the sample average? i) 640 ii) 40 iii) 0.4 iv) Impossible to calculate since the data does not follow the normal curve. d) Suppose 100 researchers each took a random sample of 1600 college students and each computed 95% confidence intervals, about how many of the confidence intervals would cover the average number of drinks all college students consumed in the past 2 weeks? i) All of them ii) 95 iii) 50 iv) 5 v) None of them since the data doesn’t follow the normal curve. e) The researchers computed 3 confidence intervals: a 68% CI, an 80% CI and a 95% CI from the same sample of 1600. The longest one is the _________CI and the shortest one is the __________CI. Fill in the blank with 68%, 80% or 95%. f) If the study asked the 1600 students whether or not they drank at all during the past 2 weeks the relevant box model would contain tickets with i) Only “1”s and “0”s ii) Numbers ranging from about 0 to 100 g) If the study asked: “Think about all the times you’ve done something that you later regretted. What percent of those times was alcohol involved?” the relevant box model would be i) Only “1”s and “0”s ii) Numbers ranging from 0 to 100 Question 12- pertains to the following situation: SKIP this one , it’s from Ch 24 which we didn’t cover Suppose a bag of moon dust is weighed 25 times. The average of the 25 weighings is 500 grams with a SD of 10 milligrams. (You may assume the Gauss model with no bias.) a) The number of tickets in the relevant box model is i) 25 ii)100 iii)Unspecified, but very large b) The draws are made ________ replacement. i) With ii) Without c) The SE for the average of the measurements is ____________milligrams. i)10 ii) 50 iii) 2 d) We can be 95% sure that the true weight of the dust is in the interval i) 500 grams +/- 40 milligrams ii) 500 grams +/- 4 milligrams iii) 500 grams +/- 400 milligrams e) If we measured the dust a 26th time then there's about a 95% chance that we'd get a weight in the interval 500 grams +/- 4 milligrams. 7 of 7 pages (12 problems)