AP Statistics 2009 Free-Response Questions - College Board

1 AP Statistics 2009 Free-Response Questions The College Board The College Board is a not-for-profit membership association whose mission is to connect students to College success and opportunity. Founded in 1900, the association is composed of more than 5,600 schools, colleges, universities and other educational organizations. Each year, the College Board serves seven million students and their parents, 23,000 high schools and 3,800 colleges through major programs and services in College readiness, College admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT , the PSAT/NMSQT and the Advanced Placement Program (AP ). The College Board is committed to the principles of excellence and equity, and that commitment is embodied in all of its programs, services, activities and concerns. 2009 The College Board . All rights reserved. College Board , Advanced Placement Program, AP, AP central , SAT, and the acorn logo are registered trademarks of the College Board .

2 PSAT/NMSQT is a registered trademark of the College Board and National Merit Scholarship Corporation. Permission to use copyrighted College Board materials may be requested online at: Visit the College Board on the Web: AP central is the official online home for the AP Program: 2009 AP Statistics Free-Response Questions -2- Formulas begin on page 3. Questions begin on page 6. Tables begin on page 11. 2009 AP Statistics Free-Response Questions -3- Formulas (I) Descriptive Statistics xixn = ()211xsxxin=- - ()()()()221212121111pnsn ssnn-+-=-+ - 01 ybbx=+ ()()()12iiixxy ybxx --=- 01bybx=- 11iixyxxyyrnss --=- 1yxsbrs= ()()221 2iibiyynsxx --=- 2009 AP Statistics Free-Response Questions -4- (II) Probability ()()()()PA BPAPBPA B = + - ()()()PA BPABPB = ()EXxpxii== ()22 Var( )xixXxpis== - If X has a binomial distribution with parameters n and p, then: ()(1)nknkPX kppk -==- npx= (1)nppxs=- pp= (1) pppns-= If x is the mean of a random sample of size n from an infinite population with mean and standard deviation ,s then: x= xnss= 2009 AP Statistics Free-Response Questions -5- (III) Inferential Statistics standard deviation of statisticstatistic parameterStandardized test statistic.

3 - ()()Confidence interval: statistic critical valuestandard deviation of statistic Single-Sample Statistic Standard Deviation of Statistic Sample Mean ns Sample Proportion (1)ppn- Two-Sample Statistic Standard Deviation of Statistic Difference of sample means 221212nnss+ Special case when 12ss= 1211nns+ Difference of sample proportions 112 212(1)(1)ppp pnn--+ Special case when 12pp= ()1pp-1211nn+ ()2observedexpectedChi-square test statisticexpected-= 2009 AP Statistics Free-Response Questions 2009 The College Board . All rights reserved. Visit the College Board on the Web: GO ON TO THE NEXT PAGE. -6- Statistics SECTION II Part A Questions 1-5 Spend about 65 minutes on this part of the exam. Percent of Section II score 75 Directions: Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.

4 1. A simple random sample of 100 high school seniors was selected from a large school district. The gender of each student was recorded, and each student was asked the following Questions . 1. Have you ever had a part-time job? 2. If you answered yes to the previous question, was your part-time job in the summer only? The responses are summarized in the table below. Gender Job Experience Male Female Total Never had a part-time job 21 31 52 Had a part-time job during summer only 15 13 28 Had a part-time job but not only during summer 12 8 20 Total 48 52 100 (a)

5 On the grid below, construct a graphical display that represents the association between gender and job experience for the students in the sample. 2009 AP Statistics Free-Response Questions 2009 The College Board . All rights reserved. Visit the College Board on the Web: GO ON TO THE NEXT PAGE. -7- (b) Write a few sentences summarizing what the display in part (a) reveals about the association between gender and job experience for the students in the sample. (c) Which test of significance should be used to test if there is an association between gender and job experience for the population of high school seniors in the district? State the null and alternative hypotheses for the test, but do not perform the test. 2. A tire manufacturer designed a new tread pattern for its all-weather tires. Repeated tests were conducted on cars of approximately the same weight traveling at 60 miles per hour. The tests showed that the new tread pattern enables the cars to stop completely in an average distance of 125 feet with a standard deviation of feet and that the stopping distances are approximately normally distributed.

6 (a) What is the 70th percentile of the distribution of stopping distances? (b) What is the probability that at least 2 cars out of 5 randomly selected cars in the study will stop in a distance that is greater than the distance calculated in part (a) ? (c) What is the probability that a randomly selected sample of 5 cars in the study will have a mean stopping distance of at least 130 feet? 3. Before beginning a unit on frog anatomy, a seventh-grade biology teacher gives each of the 24 students in the class a pretest to assess their knowledge of frog anatomy. The teacher wants to compare the effectiveness of an instructional program in which students physically dissect frogs with the effectiveness of a different program in which students use computer software that only simulates the dissection of a frog. After completing one of the two programs, students will be given a posttest to assess their knowledge of frog anatomy. The teacher will then analyze the changes in the test scores (score on posttest minus score on pretest).

7 (a) Describe a method for assigning the 24 students to two groups of equal size that allows for a statistically valid comparison of the two instructional programs. (b) Suppose the teacher decided to allow the students in the class to select which instructional program on frog anatomy (physical dissection or computer simulation) they prefer to take, and 11 students choose actual dissection and 13 students choose computer simulation. How might that self-selection process jeopardize a statistically valid comparison of the changes in the test scores (score on posttest minus score on pretest) for the two instructional programs? Provide a specific example to support your answer. 2009 AP Statistics Free-Response Questions 2009 The College Board . All rights reserved. Visit the College Board on the Web: GO ON TO THE NEXT PAGE. -8- 4. One of the two fire stations in a certain town responds to calls in the northern half of the town, and the other fire station responds to calls in the southern half of the town.

8 One of the town council members believes that the two fire stations have different mean response times. Response time is measured by the difference between the time an emergency call comes into the fire station and the time the first fire truck arrives at the scene of the fire. Data were collected to investigate whether the council member s belief is correct. A random sample of 50 calls selected from the northern fire station had a mean response time of minutes with a standard deviation of minutes. A random sample of 50 calls selected from the southern fire station had a mean response time of minutes with a standard deviation of minutes. (a) Construct and interpret a 95 percent confidence interval for the difference in mean response times between the two fire stations. (b) Does the confidence interval in part (a) support the council member s belief that the two fire stations have different mean response times? Explain. 5. For many years, the medically accepted practice of giving aid to a person experiencing a heart attack was to have the person who placed the emergency call administer chest compression (CC) plus standard mouth-to-mouth resuscitation (MMR) to the heart attack patient until the emergency response team arrived.

9 However, some researchers believed that CC alone would be a more effective approach. In the 1990s a study was conducted in seattle in which 518 cases were randomly assigned to treatments: 278 to CC plus standard MMR and 240 to CC alone. A total of 64 patients survived the heart attack: 29 in the group receiving CC plus standard MMR, and 35 in the group receiving CC alone. A test of significance was conducted on the following hypotheses. 0H: The survival rates for the two treatments are equal. H:a The treatment that uses CC alone produces a higher survival rate. This test resulted in a p-value of (a) Interpret what this p-value measures in the context of this study. (b) Based on this p-value and study design, what conclusion should be drawn in the context of this study? Use a significance level of = (c) Based on your conclusion in part (b), which type of error, Type I or Type II, could have been made? What is one potential consequence of this error?

10 2009 AP Statistics Free-Response Questions 2009 The College Board . All rights reserved. Visit the College Board on the Web: GO ON TO THE NEXT PAGE. -9- Statistics SECTION II Part B Question 6 Spend about 25 minutes on this part of the exam. Percent of Section II score 25 Directions: Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. 6. A consumer organization was concerned that an automobile manufacturer was misleading customers by overstating the average fuel efficiency (measured in miles per gallon, or mpg) of a particular car model. The model was advertised to get 27 mpg. To investigate, researchers selected a random sample of 10 cars of that model. Each car was then randomly assigned a different driver. Each car was driven for 5,000 miles, and the total fuel consumption was used to compute mpg for that car.