Multiple Choice 1. Which of the following situations qualifies as an observational study? (A) The girls at your high school are surveyed to determine if they believe there is any sexual stereotyping in the school newspaper. (B) Two flowerpots are planted with the same type of seed. One is given 0.2 cups of water each day while the other is given 0.5 cups of water each day. At the end of one month, the growth of each plant is observed and measured. (C) A team of researchers records the number and type of cars that pass a specific intersection. (D) A student flips a coin 100 times and records the number of heads. (E) None of these are observational studies. 2. Which of the following is not a requirement of a controlled experiment? (A) control (B) comparison (C) replication (D) randomization (E) All of these are required. 3. You have been given the task of determining if righthanded persons have stronger right hands than left hands. A sample of 10 right- handed persons is selected randomly. Which of the following designs would be most appropriate for this study? (A) an observational study. (B) a design blocked for gender to determine if righthand strength differs by gender. (C) a matched pair blocked experiment in which each subject represents a block wherein the strength of the right hand and the left hand is measured in random order. (D) five of the subjects are randomly placed in the control group and the other in the treatment group. All are tested and the results of each group are compared. (E) None of these is appropriate. Use the following information to answer questions 4 and 5. A research team wished to compare performance in AP Statistics based on whether the students were taught using activity-based or traditional lecture methods. The final grades in AP Statistics for 500 students were collected. 4. The population of interest is: (A) the 500 students chosen. (B) the students taught by activity-based methods. (C) the students taught by traditional lecture methods. (D) all students in high school. (E) none of these. 5. An appropriate design for the study is: (A) a blocked designed experiment. (B) a stratified random sample. (C) a completely randomized design. (D) a simple random sample. (E) none of these. 6. The three principles of experimental design include: (A) control, randomization, and double blindness (B) control, randomization, and replication (C) control, replication, and simple random sampling (D) randomization, replication, and homogeneity (E) control, randomization, and homogeneity 7. A randomized block design is not (A) similar to a stratified random sample for surveys. (B) a strategy to control for an influence that would affect the outcome of the experiment. (C) a strategy that depends on randomization. (D) only used for gender comparisons. (E) All of these describe a randomized block design. 8. Which one of the following statements about experiments is true? (A) All experiments must have a control group. (B) Blocking is employed to reduce variation. (C) Random assignment is only critical for treatment groups, as opposed to control groups. (D) Matching can be used in any experiment to eliminate lurking variables. (E) None of these is true. 9. In an experiment, if two variables are confounded, which of the following statements is true? (A) One of the variables must be a lurking variable. (B) The variables will have a correlation coefficient greater than ±.5. (C) There is a clear indication that a placebo effect is present in the experiment. (D) The investigator cannot separate the effect of the variables on a response variable. (E) None of these is true. 10. When subjects in both the treatment and control group exhibit favorable responses, the condition is an example of (A) the Hawthorne effect, an improvement merely because of a change from the status quo. (B) the placebo effect. (C) an experiment that is confounded. (D) the regression fallacy. (E) blocking to reduce variation. 11. A randomized block design is similar to which of the following sampling designs? (A) simple random sample (B) multistage cluster sample (C) stratified sample (D) convenience sample (E) systematic sample 12. Blocking is utilized to help (A) organize the treatment and control groups. (B) counteract the placebo effect. (C) produce groups that are as similar as possible. (D) replicate the experiment within each block. (E) avoid the need for randomization.
13. An advantage to using surveys as opposed to experiments is that (A) surveys are generally cheaper to conduct. (B) it is generally easier to conclude cause and effect from surveys. (C) surveys are generally not subject to bias. (D) surveys involve use of randomization. (E) surveys can make use of stratification. 14. Two studies are run to compare the experiences of lowincome families receiving food stamps to those receiving cash subsidies. The first study interviews 50 families who have been in each government program for at least 2 years, while the second randomly assigns SO families to each program and interviews them after 2 years. Which of the following is a true statement? (A) Both studies are observational studies because of the time period involved. (B) Both studies are observational studies because there are no control groups. (C) The first study is an observational study; the second is an experiment. (D) The first study is an experiment; the second is an observational study. (E) Both studies are experiments, because in each, families are receiving treatments (food stamps or cash). 15. In a study of Parkinson's disease, 100 volunteers had incisions made through their skulls. The patients were randomly sorted into two groups, one of which had a new drug inserted into the brain. In the other group, the skulls were closed with no treatment given. The patients did not know who received the drug. In the weeks to follow all 1 00 volunteers showed similar improvement in physical condition. What is this an example of? (A) The effect of a treatment unit (B) The placebo effect (C) The control group effect (D) Sampling error (E) Voluntary response bias 16. Fifty migraine patients are randomly selected from hospital records. Half the patients are told to drink ice water and sit in the dark when they next experience a migraine; the remaining patients are told to use neither of these possible remedies. Participants then report back as to relief, if any. Faults of this experimental design include all of the following except: (A) Lack of randomization (B) Confounding variables (C) Lack of blinding (D) Unclear factor levels (E) Measurement of response variable 17. Which of the following is most useful in establishing cause-and-effect relationships? (A) A complete census (B) A least squares regression line showing high correlation (C) A simple random sample (SRS) (D) A well-designed, well-conducted survey incorporating chance to ensure a representative sample (E) A controlled experiment 18. Sampling error occurs (A) when interviewers make mistakes resulting in bias. (B) when interviewers use judgment instead of random choice in picking the sample. (C) when samples are too small. (D) because a sample statistic is used to estimate a population parameter. (E) in all of the above cases. Free Response 19. A researcher wishes to determine if there is a difference in the voting patterns of teachers. She wishes to determine whether teachers in rural, suburban, or urban schools tend to vote more often for Democrats, Republicans, or Independents. In addition, she believes that years of graduate education influence voting patterns. However, the effect of years of graduate education is not the primary focus of the study. a. Can her study be considered an experiment? Explain your answer. b. Identify the explanatory and response variables in this study. Indicate the levels of the explanatory variable. c. Describe how the sample can be selected using a simple random sample. d. Describe how the data can be collected in a stratified random sample. 20. A new drug to treat hypertension (high blood pressure) is to be tested. Baseline blood pressures of the subjects are to be taken at the beginning of the study and readings will subsequently be taken once per week for the duration of the study. Preliminary indications suggest that the effectiveness of the drug in reducing high blood pressure may depend on age (young, middle, or elderly). a. Draw a graphic of how you would form the treatment and control groups for this test. b. Draw a graphic of how you would form the treatment and control groups if you wish to control for both age and gender. 21. An investigator wants to study the effectiveness of two surgical procedures to correct nearsightedness: procedure A uses cuts from a scalpel and procedure B uses a laser. The data to be collected are the degrees of improvement in vision after the procedure is performed. a. Describe how the investigator can design an experiment using independent samples. b. Describe how the investigator can design an experiment using matched pairs.
c. Which technique would provide the most valuable information about the effectiveness of each procedure? Explain your reasoning. d. For this study to be an experiment, the assignment of subjects into treatment and control should be accomplished randomly. Describe the ethical difficulty involved with random assignment in this situation. 22. A hothouse for young plants has immovable planting beds and artificial lights as indicated in the figure below: A new quick-grow fertilizer is to be tested in the hothouse. The treatment group is administered the new fertilizer while the control group receives the traditional fertilizer. All other conditions (cultivating, water, and so on) are applied uniformly to both groups of beds. Describe how you would assign the beds to the treatment and control group so that the amount of light does not confound the result. Also discuss the consequences of your design relative to the analysis of data. 23. A survey is to be conducted in your high school. There is to be a total of 40 students in the sample. Describe how you would choose the participants if: a. there are to be the same number of freshmen, sophomores, juniors, and seniors in the sample. b. there are to be the same number of males and females in the sample. c. there are no restrictions on the choice of the participants. 24. A medical researcher is interested in testing a new medicine for migraine headaches. She decides to conduct a clinical trial on 100 randomly selected adults who get migraine headaches at a rate of one per week or more. Although age and gender are not of primary interest in the trials, the researcher is concerned that these factors may impact the effectiveness of the drug. a. Describe how she should set up her experiment for the 100 subjects without considerations of age and gender. (A graphic is an acceptable answer.) b. Describe how she should set up her experiment for the 100 subjects if she wishes to control for gender. (A graphic is an acceptable answer.) c. Describe how she should set up her experiment for the 100 subjects if she wishes to control for age. She decides on age categories of young (21-35), middle (36-55) and elderly (over 55). (A graphic is an acceptable answer.) d. Describe how she should set up her experiment for the 100 subjects if she wishes to control both for age and gender. (A graphic is an acceptable answer.) Each case 25 26 listed below is an example of a flawed conclusion from an observational study. Comment on each study, focusing particularly on any possible variables that may have been present that may be confounded with the variable of interest. Choose one of the possible confounding variables you have identified and suggest how grouping of subjects may address the confounding. 25. A study determines that deaths due to lung ailments occur more frequently in cities than in rural areas. The study concludes that air pollution in cities is detrimental to one's health. 26. A study compared the frequency of riots and the high temperature on the first day that the riot occurred. It was found that the frequency of riots was significantly less on days whose high temperature was greater than 100 degrees. The conclusion was made that high temperatures deter riots. 27. Describe how you would design both an observational study and an experiment for the following question: The popping rates of three popular brands of popcorn are to be studied so that a conclusion about the brand with the greatest popping rate can be determined. If either design is not possible, explain why. 28. An experiment to determine the effect of a fertilizer on the growth of grass is to be conducted in a controlled environment. Identical soil and seeds are placed in plots that are attached to immovable laboratory tables as the figure below indicates. Once the grass shoots appear, some plots are treated with the fertilizer while the rest receive no fertilizer. All other conditions regarding water, temperature, etc. are identical except for the proximity of the single light source to the plots. In the figure, each rectangle represents a test plot. The light source is indicated by the shaded circle in the drawing of the test site. Describe how the experiment should be designed so that the intensity of the light is not a confounding variable. 29. A guidance counselor conducts a study to determine the effect of caloric intake at breakfast on alertness in firstperiod classes. She interviews an SRS of 20 students who claim to eat under 1,000 calories at breakfast, and an SRS of 20 students who claim to eat over 1,000 calories at breakfast. In each group, she measures alertness on a standard scientific scale. a. Explain why this is an observational study and not an experiment. b. Give an example of a possible confounding variable with an explanation in the context of this study. c. If the students who eat over 1,000 calories test higher on the alertness scale, is it reasonable to encourage all students to eat larger breakfasts?
d. How could the counselor design a related experiment to study caloric intake at breakfast with alertness in first period? 30. A high school math department conducts a study to determine whether a new AP Statistics textbook will lead to higher AP exam scores than the textbook currently in use. Two AP statistics classes are scheduled, each teacher has 18 students, and it is randomly decided which class will use which book. At the end of the academic year, the 18 students in each class take the AP Statistics, exam, and the department notes the scores. a. Identify the response variable, the treatments, and the experimental units. b. Was randomization properly used? Explain. c. Was replication properly used? Explain. d. Teacher is a confounding variable. Explain. 31. A high school math teacher believes the greater the number of hours of sleep before taking an AP exam, the better the score. She interviews the 18 students taking her AP Statistics class the day after the exam and later notes their scores. a. Is this an observational study or an experiment? Explain. b. Comment on the design of the study.
Answers 1. C 7. D 13. A 2. E 8. B 14. C 3. C 9. D 15. B 4. E 10. B 16. C 5. C 11. C 17. E 6. B 12. C 18. B 19. a. No. No treatments were imposed. b. Explanatory: location; Response: voting preference. Levels of the explanatory variable: rural, suburban, urban. c. Answers will vary. Be careful to make sure that all teachers in all settings have a chance to be included in the sample. d. Run a simple random sample within rural schools, suburban schools, and urban schools. 20. Answers will vary. An example of a correct answer is block arrangement, data from each pairing should be compared and analyzed separately. 23. a. Select a simple random sample of 10 from each class. b. Select a simple random sample of 20 males and a simple random sample of 20 females. c. Select a simple random sample of size 40. 24. Answers may vary. Possible correct graphics are shown below. b. b. c. d. 21. a. The investigator can randomly place individuals interested in the surgery into groups for procedure A and for procedure B. Perform the surgeries and monitor the degree of improvement for each group. Compare the mean degree of improvement for each group. b. Perform procedure A on one eye, randomly selected, and procedure B on the other eye and compare the difference in the degrees of improvements of each eye (the A eye - the B eye) for each participant. c. Answers will vary. d. Answers will vary but should focus on the recruitment of subjects for each group. 22. Answers may vary. One possible correct answer would be to block beds (1, 4), (2, 5), and (3, 6). Within each pair, assignment of beds to the new fertilizer or the traditional fertilizer should be accomplished randomly. A coin could be flipped; random digit tables could be used; or a random number generator could be employed as well. With the
25. There could be many lurking variables such as pace of life, levels of stress, diet, lack of exercise, etc. 26. In a temperate climate, there are fewer very hot days each year during which a riot could occur. 27. Answers will vary. One possible design for the observational study might be: Randomly select 200 kernels of each brand and pop them in the same popper. Count the number of unpopped kernels when finished. Make sure that the popper is cool before starting each popping session. An experiment is not possible since the investigator cannot impose the brands on the kernels. 28. Answers may vary. A good design would be to block 1-3-10-12; 4-6-7-9; 2-11; 5-8; and randomly assign fertilizers within each block. Correct answers should clearly indicate blocking in such a way that lighting effect is the same for all flowerbeds. 29. (a) No treatment is being imposed on anyone. (b) There are many possible answers. For example, it is possible that the students eating under 1,000 calories are those who sleep in late, have to rush to school without eating, and have not fully awakened during first period. (c) No, because cause-and-effect conclusions cannot be drawn from observational studies. (d) Randomly select a group of students who are told they must eat under 1,000 calories at breakfast, and randomly select another group who are told they must eat over 1,000 calories at breakfast. Compare alertness levels in first-period classes. 30. (a) The response variable is the exam scores, the treatments are the two books, and the experimental units are the two classes (not the students themselves!). (b) Yes, the two books (the treatments) were randomly assigned to the two classes (the experimental units). (c) No, there was no replication in this study. Each treatment was applied to only one experimental unit. (d) If a difference in exam scores is noted between the two classes, it is not known if this is due to the difference in books or the difference in teachers. That is, the treatments (books) are confounded with the teachers. 31. (a) No treatment is being imposed, so this is an observational study. (b) This is not an SRS of students. The students were all from her class and this could have introduced bias in the way they responded about hours of sleep.