Test 4C AP Statistics Name:

Transcription

1 Test 4C AP Statistics Name: Part 1: Multiple Choice. Circle the letter corresponding to the best answer. 1. The Hemlock Woolly Adelgid is an insect that has accidentally been released in Eastern U.S. forests from Asia. Since it has no natural enemies in the U.S., it is spreading rapidly. A forester studying the abundance of the insect in southern Vermont wants to determine if it has spread that far north. He randomly selects 200 hemlock trees in a large Vermont forest and finds that 46 of them show signs of damage from this insect. It would be appropriate to generalize the results of the study to (a) all hemlock trees in southern Vermont. (b) all trees in southern Vermont. (c) the 200 hemlock trees that were randomly selected (d) all hemlock trees in the United states. (e) all hemlock trees in the forest from which the 200 trees were selected. 2. Which of the following is a method for improving the accuracy of a sample? (a) Use no more than 3 or 4 words in any question. (b) When possible, avoid the use of human interviewers, relying on computerized dialing instead. (c) Use large sample sizes. (d) Use smaller sample sizes. (e) Ask only questions for which the responses are quantitative variables. 3. We say that the design of a study is biased if which of the following is true? (a) A racial or sexual preference is suspected. (b) Random placebos have been used. (c) Certain outcomes are systematically favored. (d) The correlation is greater than 1 or less than 1. (e) An observational study was used when an experiment would have been feasible. 4. A sample of student opinion at a Big Ten university selects an SRS of 200 of the 30,000 undergraduate students and a separate SRS of 100 of the 5,000 graduate students. This kind of sample is called a (a) simple random sample. (b) simple random sample with blocking. (c) multistage random sample. (d) stratified random sample. (e) random cluster sample. 5. A recent survey by a large-circulation Canadian magazine on the contribution of universities to the economy was circulated to 394 people who the magazine decided are the most likely to know how important universities are to the Canadian economy. The main problem with using these results to draw conclusions about the general public s perception is (a) insufficient attention to the placebo effect. (b) no control group. (c) lack of random assignment BFW Publishers The Practice of Statistics, 4/e- Chapter 4 187

2 (d) lack of random selection. (e) response bias. 6. For a certain experiment you have 8 subjects, of which 4 are female and 4 are male. The name of the subjects are listed below: Males: Atwater, Bacon, Chu, Diaz. Females: Johnson, King, Liu, Moore There are to be two treatment groups, A and B. If a randomized block design is used, with the subjects blocked by their gender, which of the following is not a possible group of subjects for treatment group A? (a) Atwater, Chu, King, Liu (b) Bacon, Chu, Liu, Moore (c) Atwater, Diaz, Liu, King (d) Atwater, Bacon, Chu, Johnson (e) Atwater, Bacon, Johnson, King 7. A Texas school district wants to compare the effectiveness of a standard AP Statistics curriculum and a new hands-on AP Statistics curriculum. Two experienced teachers, Mr. Pryor and Mr. Legacy, each teach one class with the standard curriculum and one with the new approach. Students are assigned at random to these four classes. At the end of the year, all students take the AP Statistics exam. The subjects in this experiment are (a) Mr. Pryor and Mr. Legacy. (b) the two AP Statistics curricula. (c) the students in the four classes. (d) all students taking AP Statistics in Texas. (e) only one: AP Statistics. 8. The Texas experiment described in the previous question (a) has one factor: the type of AP Statistics curriculum a student is assigned to. (b) has two factors: the type of AP Statistics curriculum and the teacher a student is assigned to. (c) has two factors: the standard curriculum and one with the hands-on approach. (d) has three factors: the type of AP Statistics curriculum, the teacher, and the class a student is assigned to. (e) has three factors: the standard curriculum, the hands-on approach, and the teacher a student is assigned to. 188 The Practice of Statistics, 4/e- Chapter BFW Publishers

3 9. A materials engineer wishes to compare the durability of two different types of paving material. She has 40 different one-mile stretches of interstate highway that she s been authorized to repave for this study. She decides to carry out a matched pairs experiment. Which of the following is the best way for her to carry out the randomization for this study? (a) Use a table of random digits to divide the 40 roadways into 20 pairs and then, for each pair, flip a coin to decide which pavement to use on which member of the pair. (b) Subjectively divide the 40 roadways into 20 pairs (making the roadways within each pair as different as possible) and then, for each pair, flip a coin to decide which pavement to use on which member of the pair. (c) Use a table of random digits to divide the 40 roadways into two groups of twenty, and then use the table of random digits a second time to decide which pavement to use on which group. (d) Let each of the 40 roadways act as its own pair, dividing each roadway into the first halfmile and the second half-mile. Flip a coin for each of the 40 roadways to decide which half-mile gets which pavement. (e) Let each of the 40 roadways act as its own pair, dividing each roadway into the first halfmile and the second half-mile. Flip a coin once to decide which pavement is put on the first half-mile of all the roadways. 10. An article in the student newspaper of a large university had the headline A's swapped for evaluations? The article included the following. According to a new study, teachers may be more inclined to give higher grades to students, hoping to gain favor with the university administrators who grant tenure. The study examined the average grade and teaching evaluation in a large number of courses in order to investigate the effects of grade inflation on evaluations. I am concerned with student evaluations because instruction has become a popularity contest for some teachers, said Professor Smith, who recently completed the study. Results showed that higher grades directly corresponded to a more positive evaluation. Which of the following would be a valid conclusion to draw from the study? (a) A teacher can improve his or her teaching evaluations by giving good grades. (b) A good teacher, as measured by teaching evaluations, helps students learn better, resulting in higher grades. (c) Teachers of courses in which the mean grade is above average apparently tend to have above-average teaching evaluations. (d) Teaching evaluations should be conducted before grades are awarded. (e) All of the above BFW Publishers The Practice of Statistics, 4/e- Chapter 4 189

4 Part 2: Free Response 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. 11. In a 1995 Corporation for Public Broadcasting poll of TV viewership, one question was, A recent study by a psychology professor at a leading university concluded that the amount of violence children see on television has an effect on their likelihood of being aggressive and committing crimes. From what you have seen or heard about this subject, do you agree strongly with that conclusion, agree somewhat, or disagree strongly? Is this question appropriate, or is it flawed in some way? Comment briefly. 12. The Student Council has been asked to determine the attitude of the students at your school toward a new dress code policy. Joe, a member of the council who is taking AP Statistics, decides to send a questionnaire to an SRS of 100 students. Eighty-seven students return the completed questionnaire. Joe decides to randomly select 13 additional students to serve as replacement subjects to complete the sample of 100. Is Joe s sampling method appropriate? Briefly comment on the merits of this method or its pitfalls. 13. Here s a quick and easy way to randomize. You have 100 subjects, 50 women and 50 men. Toss a coin. If it s heads, assign the men to the treatment and the women to the control group. If the coin comes up tails, assign the women to treatment and the men to control. This gives every individual subject a chance of being assigned to treatment or control. Is this a reasonable way to randomly assign subjects to treatment groups? Explain your reasoning. 190 The Practice of Statistics, 4/e- Chapter BFW Publishers

5 14. Does ginkgo improve memory? The law allows marketers of herbs and other natural substances to make health claims that are not supported by evidence. Brands of ginkgo extract claim to improve memory and concentration. A randomized comparative experiment found no statistically significant evidence for such effects. The subjects were 230 healthy volunteers over 60 years old. They were randomly assigned to ginkgo or a placebo pill (a dummy pill that looks and tastes the same). All the subjects took a battery of tests for learning and memory before treatment started and again after six weeks. (a) The study was double-blind. What does this mean? (b) Comment briefly on the extent to which results of this study can be generalized to some larger population, and the extent to which cause and effect has been established. (c) Explain why it is advantageous to use 230 volunteers in this study, rather than, say, 30. (d) Explain what the expression no statistically significant evidence means in the context of this study. (e) Using the random digits below (starting at line 103), choose the first four members of the ginkgo group. Explain your method BFW Publishers The Practice of Statistics, 4/e- Chapter 4 191

6 treatment, and the remaining subjects will receive a commonly-used standard treatment. Compare relief from migraine pain between the treatment group and the control group. 13. (a) Wording of question bias: it s possible that using the phrase government censorship of artistic expression generates a positive response more often than a more neutral phrase, so that 85% is an overestimate of support. (b) Because the survey is only given to people over 50 who have paid to join AARP, the survey suffers from undercoverage of the young and those who do not have enough income to pay for membership in AARP. Thus the survey will probably underestimate support for the program. (There are other plausible answers, such as wording of the question or response bias). Test 4C Part 1 1. e The sample is limited to 200 hemlock trees randomly selected from this particular forest. We can only generalize about trees in the population from which the sample was taken. 2. c Larger sample sizes reduce variability from sample to sample, thereby increasing accuracy of any single sample. 3. c This is the definition of bias see text page d The strata are undergraduate and graduate students. Answer (b) is a common mistake: blocking refers to experiments, stratification refers to sampling. 5. d Surveying people who are most likely to know how important universities are is not random selection, therefore inferences about the population cannot be made. 6. d If the subjects are blocked by gender, then each treatment group should have two males and two females. 7. c Individual students are randomly assigned to classes, and the response variable is measured on each student. 8. b The classes are the treatment groups, and the treatments teacher and curriculum are assigned to those groups. 9. d This method results in 40 matched pairs, with pavement types assigned randomly within each pair. [(a) does not match the pairs; (b) pairs roadways with different characteristics, not similar; (c) is a completely randomized design; (e) does not properly randomize within each pair. 10. c Since the evaluations are a sample survey, not an experiment, cause and effect cannot be inferred in the association between evaluations and grades. Part Question is flawed because it includes a position that leads a participant towards a certain response, introducing bias. 12. No, it introduces non-response bias. If the 13 students who didn t respond all held similar opinions, adding 13 newly-selected students would not accurately represent the views of the original The method completely confounds gender with whatever the treatment is, since all the males are in one group and all the females are in the other. It will be impossible to separate the effect of the treatment from the effects due to gender. 14. (a) Neither the subjects nor the researchers who administered the learning and memory tests knew which subjects were taking the gingko extract and which were taking the placebo. (b) Since subjects were randomly assigned to groups, we can make inferences about cause and effect. But because the subjects were volunteers and not randomly selected from the population (healthy people over 60), we cannot make inferences about the population as a whole. (c) A larger number of subjects greater replication decreases the impact of random variation on 2011 BFW Publishers The Practice of Statistics, 4/e- Chapter 4 197

7 experimental results, thereby increasing our ability to distinguish the effects of the treatment. (d) No statistical significance means that the differences found in memory and concentration between subjects in the two treatments was small enough so that it could be attributable to variation between randomly-assigned subjects, rather than an effect of the treatment. (e) Assign the volunteers numbers from 001 to 230. Starting on line 103, choose 3-digit numbers from the table, ignoring unassigned numbers and repeats, until you have selected 115 numbers for the treatment group. By this method, the first five numbers are 170, 005, 227, 118, The Practice of Statistics, 4/e- Chapter BFW Publishers