2008年统计模拟题选择题

The questions contained in this AP® Statistics Practice Exam are written to the content specifications of AP Exams for this subject. Taking this practice exam should provide students with an idea of their general areas of strengths and weaknesses in preparing for the actual AP Exam. Because this AP Statistics Practice Exam has never been administered as an operational AP Exam, statistical data are not available for calculating potential raw scores or conversions into AP grades. This AP Statistics Practice Exam is provided by the College Board for AP Exam preparation. Teachers are permitted to download the materials and make copies to use with their students in a classroom setting only. To maintain the security of this exam, teachers should collect all materials after their administration and keep them in a secure location. Teachers may not redistribute the files electronically for any reason. © 2008 The College Board. All rights reserved. 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Practice Exam Advanced Placement Program AP® Statistics Contents Directions for Administration ............................................................................................ ii Section I: Multiple-Choice Questions................................................................................ 1 Section II: Free-Response Questions ...............................................................................46 Student Answer Sheet for Multiple-Choice Section .......................................................64 Multiple-Choice Answer Key............................................................................................65 Free-Response Scoring Guidelines...................................................................................66 The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. 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AP Central is the official online home for the AP Program: apcentral.collegeboard.com. -i- AP® Statistics Directions for Administration The AP Statistics Exam is three hours in length and consists of a multiple-choice section and a free-response section. • The 90-minute multiple-choice section contains 40 questions and accounts for 50 percent of the final grade. • The 90-minute free-response section contains 6 questions and accounts for 50 percent of the final grade. Students should be given a 10-minute warning prior to the end of each section of the exam. A 10-minute break should be provided after Section I is completed. The actual AP Exam is administered in one session. Students will have the most realistic experience if a complete morning or afternoon is available to administer this practice exam. If a schedule does not permit one time period for the entire practice exam administration, it would be acceptable to administer Section I one day and Section II on a subsequent day. Many students wonder whether or not to guess the answers to the multiple-choice questions about which they are not certain. It is improbable that mere guessing will improve a score. However, if a student has some knowledge of the question and is able to eliminate one or more answer choices as wrong, it may be to the student’s advantage to answer such a question. • The use of approved calculators is permitted during the exam. More information on calculators that are approved for use on this exam can be found on AP Central. • It is suggested that the practice exam be completed using a pencil to simulate an actual administration. • Teachers will need to provide paper for the students to write their free-response answers. Teachers should provide directions to the students indicating how they wish the responses to be labeled so the teacher will be able to associate the student’s response with the question the student intended to answer. • Remember that students are not allowed to remove any materials, including scratch work, from the testing site. -ii- Section I Multiple-Choice Questions -1- Formulas begin on page 3. Questions begin on page 6. Tables begin on page 42. -2- Formulas (I) Descriptive Statistics x xi n= ∑ s n xi xx = − −∑ 1 1 2d i s n s n s n np = − + − − + − 1 2 1 2 2 2 1 2 1 1 1 1 d i d i d i d i �y b b x= +0 1 b x x y y x x i i i 1 2 = − − − ∑ ∑ d id i d i b y b x0 1= − r n x x s y y s i x i y = − − −F HG I KJ∑ F HG I KJ 1 1 b r s s y x1 = s y y n x x b i i i 1 2 2 2 = − − − ∑ ∑ �d i d i -3- (II) Probability ( ) ( ) ( ) ( )P A B P A P B P A B» = + - « ( )( ) ( ) P A BP A B P B «= ( )E X x px i i= = Âμ ( )22Var( ) x i xX x pi= = -Âs μ If X has a binomial distribution with parameters n and p , then: ( ) (1 )n k n kP X k p p k Ê ˆÁ ˜Ë ¯ -= = - npx =μ (1 )np p x = -s ˆ pp =μ (1 ) ˆ p p p n -=s If x is the mean of a random sample of size n from an infinite population with mean μ and standard deviation ,s then: x =μ μ x n = ss -4- (III) Inferential Statistics Standardized test statistic: statistic parameter standard deviation of statistic - Confidence interval: statistic critical value standard deviation of statistic± ( ) ( )∑ Single-Sample Statistic Standard Deviation of Statistic Sample Mean σ n Sample Proportion p p n ( )1 − Two-Sample Statistic Standard Deviation of Statistic Difference of sample means σ σ1 2 1 2 2 2n n + Special case when σ σ1 2= σ 1 1 1 2n n + Difference of sample proportions p p n p p n 1 1 1 2 2 2 1 1( ) ( )− + − Special case when p p1 2= p p1−b g 1 1 1 2n n + Chi-square test statistic observed expected expected= −∑ a f2 -5- GO ON TO THE NEXT PAGE. STATISTICS SECTION I Time—1 hour and 30 minutes Number of questions—40 Percent of total grade—50 Directions: Solve each of the following problems, using the available space for scratch work. Select the answer choice that is best in each case and place the letter of your choice in the corresponding box on the student answer sheet. Do not spend too much time on any one problem. 1. The dotplot below displays the total number of miles that the 28 residents of one street in a certain community traveled to work in one five-day workweek. Which of the following is closest to the percentile rank of a resident from this street who traveled 85 miles to work that week? (A) 60 (B) 70 (C) 75 (D) 80 (E) 85 -6- GO ON TO THE NEXT PAGE. 2. A large simple random sample of people aged nineteen to thirty living in the state of Colorado was surveyed to determine which of two MP3 players just developed by a new company was preferred. To which of the following populations can the results of this survey be safely generalized? (A) Only people aged nineteen to thirty living in the state of Colorado who were in this survey (B) Only people aged nineteen to thirty living in the state of Colorado (C) All people living in the state of Colorado (D) Only people aged nineteen to thirty living in the United States (E) All people living in the United States -7- GO ON TO THE NEXT PAGE. 3. Janelle collected data on the amount of time in minutes each person in a large sample of customers spent in a local store. The data also included recording the gender of each customer. These data were used to generate the boxplots shown below. Which of the following statements is true? (A) The range in the amount of time in minutes males in the sample of customers spent in the store is approximately 40 minutes. (B) The mean amount of time in minutes males in the sample of customers spent in the store is approximately 20 minutes. (C) The third quartile of the amount of time in minutes males in the sample of customers spent in the store is approximately 45 minutes. (D) The interquartile range of the amount of time in minutes females in the sample of customers spent in the store is 15 minutes. (E) Approximately half of the males in the sample of customers spent at least as much time in the store as any female in the sample of customers. -8- GO ON TO THE NEXT PAGE. 4. The probability of obtaining a head when a certain coin is flipped is about 0.65. Which of the following is closest to the probability that heads would be obtained 15 or fewer times when this coin is flipped 25 times? (A) 0.14 (B) 0.37 (C) 0.39 (D) 0.60 (E) 0.65 5. A study was conducted using data collected on the birth weights of a random sample of 10 pairs of identical twins to determine whether the twin born first tends to weigh more than the twin born second. Let mF represent the average birth weight of all twins born first, mS represent the average birth weight of all twins born second, and mD represent the average difference in birth weight (weight of first minus weight of second) for all pairs of twins. Which of the following would be the null and alternative hypotheses for this study? (A) 0H : m m=F S and aH : m mD (D) 0H : m m m- =F S D and aH : m m m- >F S D (E) 0H : m m m- =F S D and aH : m m m- πF S D -9- GO ON TO THE NEXT PAGE. 6. The buyer for an electronics store wants to estimate the proportion of defective wireless game controllers in a shipment of 5,000 controllers from the store’s primary supplier. The shipment consists of 200 boxes each containing 25 controllers. The buyer numbers the boxes from 1 to 200 and randomly selects six numbers in that range. She then opens the six boxes with the corresponding numbers, examines all 25 controllers in each of these boxes, and determines the proportion of the 150 controllers that are defective. What type of sample is this? (A) Biased random sample (B) Nonrandom sample (C) Simple random sample (D) Stratified random sample (E) Cluster random sample 7. A distribution of test scores is not symmetric. Which of the following is the best estimate of the z-score of the third quartile? (A) 0.67 (B) 0.75 (C) 1.00 (D) 1.41 (E) This z-score cannot be estimated from the information given. -10- GO ON TO THE NEXT PAGE. 8. Sophomore, junior, and senior students at a high school will be surveyed regarding a potential increase in the extracurricular student activities fee. There are three possible responses to the survey question—agree with the increase, do not agree with the increase, or no opinion. A chi-square test will be conducted to determine whether the response to this question is independent of the class in which the student is a member. How many degrees of freedom should the chi-square test have? (A) 9 (B) 6 (C) 4 (D) 2 (E) 1 -11- GO ON TO THE NEXT PAGE. 9. A certain type of remote-control car has a fully charged battery at the time of purchase. The distribution of running times of cars of this type, before they require recharging of the battery for the first time after its period of initial use, is approximately normal with a mean of 80 minutes and a standard deviation of 2.5 minutes. The shaded area in the figure below represents which of the following probabilities? (A) The probability that the running time of a randomly selected car of this type, before it requires recharging of the battery for the first time after its period of initial use, is between 75 minutes and 82.5 minutes. (B) The probability that the running time of a randomly selected car of this type, before it requires recharging of the battery for the first time after its period of initial use, is between 75 minutes and 85 minutes. (C) The probability that the running time of a randomly selected car of this type, before it requires recharging of the battery for the first time after its period of initial use, is between 77.5 minutes and 82.5 minutes. (D) The probability that the running time of a randomly selected car of this type, before it requires recharging of the battery for the first time after its period of initial use, is between 77.5 minutes and 85 minutes. (E) The probability that the running time of a randomly selected car of this type, before it requires recharging of the battery for the first time after its period of initial use, is between 77.5 minutes and 87.5 minutes. -12- GO ON TO THE NEXT PAGE. 10. Which of the following scatterplots could represent a data set with a correlation coefficient of 1?r = - (A) 200 1 2 3 4 40 60 80 100 (B) 200 1 2 3 4 40 60 80 100 (C) 200 1 2 3 4 40 60 80 100 (D) 200 1 2 3 4 40 60 80 100 (E) 200 1 2 3 4 40 60 80 100 -13- GO ON TO THE NEXT PAGE. 11. Publishers of a magazine wish to determine what proportion of the magazine’s 50,000 subscribers are pleased with their subscription. The publishers intend to mail a survey to 1,000 subscribers randomly selected from those who have received the magazine for 5 years or more. This introduces selection bias, since long-subscribing customers are more likely to be pleased with their subscription. Which of the following would best eliminate selection bias? (A) Mail surveys to 2,000 subscribers randomly selected from those who have received the magazine for 5 years or more. (B) Mail surveys to 1,000 subscribers randomly selected from those who have received the magazine for 1 year or less. (C) Mail surveys to 1,000 subscribers randomly selected from all subscribers. (D) Mail surveys to 1,000 subscribers randomly selected from those who have received the magazine for 5 years or more and 1,000 subscribers randomly selected from those who have received the magazine for 1 year or less. (E) Mail surveys to 500 subscribers randomly selected from a group who have received a free six-month subscription within the past year. -14- GO ON TO THE NEXT PAGE. 12. An environmental scientist wants to test the null hypothesis that an antipollution device for cars is not effective. Under which of the following conditions would a Type I error be committed? (A) The scientist concludes that the antipollution device is effective when it actually is not. (B) The scientist concludes that the antipollution device is not effective when it actually is. (C) The scientist concludes that the antipollution device is effective when it actually is. (D) The scientist concludes that the antipollution device is not effective when it actually is not. (E) A Type I error cannot be committed in this situation. -15- GO ON TO THE NEXT PAGE. 13. A data set of test scores is being transformed by applying the following rule to each of the raw scores. Transformed score = 3.5(raw score) + 6.2 Which of the following is NOT true? (A) The mean transformed score equals 3.5(the mean raw score) + 6.2. (B) The median transformed score equals 3.5(the median raw score) + 6.2. (C) The range of the transformed scores equals 3.5(the range of the raw scores) + 6.2. (D) The standard deviation of the transformed scores equals 3.5(the standard deviation of the raw scores). (E) The IQR of the transformed scores equals 3.5(the IQR of the raw scores). -16- GO ON TO THE NEXT PAGE. 14. A random sample of 25 households from the Mountainview School District was surveyed. In this survey, data were collected on the age of the youngest child living in each household. The histogram below displays the data collected in the survey. In which of the following intervals is the median of these data located? (A) 0 years old to less than 2 years old (B) 4 years old to less than 6 years old (C) 6 years old to less than 8 years old (D) 8 years old to less than 10 years old (E) 10 years old to less than 12 years old -17- GO ON TO THE NEXT PAGE. 15. Based on a random sample of 50 students, the 90 percent confidence interval for the mean amount of money students spend on lunch at a certain high school is found to be ($3.45, $4.15). Which of the following statements is true? (A) 90% of the time, the mean amount of money that all students spend on lunch at this high school will be between $3.45 and $4.15. (B) 90% of all students spend between $3.45 and $4.15 on lunch at this high school. (C) 90% of all random samples of 50 students obtained at this high school would result in a sample mean amount of money students spend on lunch between $3.45 and $4.15. (D) 90% of all random samples of 50 students obtained at this high school would result in a 90% confidence interval that contains the true mean amount of money students spend on lunch. (E) Approximately 45 of the 50 students in the random sample will spend between $3.45 and $4.15 on lunch at this high school. -18- GO ON TO THE NEXT PAGE. 16. Ten percent of all Dynamite Mints candies are orange and 45 percent of all Holiday Mints candies are orange. Two independent random samples, each of size 25, are selected⎯one from Dynamite Mints candies and the other from Holiday Mints candies. The total number of orange candies in the two samples is observed. What are the expected total number of orange candies and the standard deviation for the total number of orange candies, respectively, in the two samples? (A) 7 and 2.905 (B) 7 and 3.987 (C) 13.75 and 2.233 (D) 13.75 and 2.905 (E) 13.75 and 3.987 17. In a random sample of 60 shoppers chosen from the shoppers at a large suburban mall, 36 indicated that they had been to a movie in the past month. In an independent random sample of 50 shoppers chosen from the shoppers in a large downtown shopping area, 31 indicated that they had been to a movie in the past month. What significance test should be used to determine whether these data provide sufficient evidence to reject the hypothesis that the proportion of shoppers at the suburban mall who had been to a movie in the past month is the same as the proportion of shoppers in the large downtown shopping area who had been to a movie in the past month? (A) One proportion z-test (B) One sample z-test for a mean (C) One sample t-test for a mean (D) Two proportion z-test (E) Two sample t-test for means -19- GO ON TO THE NEX