AP Statistics
Name _______________________ CHAPTER 5 REVIEW
DIRECTIONS: For Multiple Choice, circle only one response. For Free Response, response needs to include proper use of statistical terminology. MULTIPLE CHOICE 1. A member of Congress wants to know what his constituents (people from their district) think of proposed legislation on health insurance. His staff reports that 228 letters have been received on the subject, of which 193 oppose the legislation. What is the population in this situation? a) The constituents. b) The 228 letters received. c) The 193 opposing the legislation. d) Congress. e) None of the above. A chemical engineer is designing the production process for a new product. The chemical reaction that produces the product may have a higher or lower yield depending on the temperature and the stirring rate in the vessel in which the reaction takes place. The engineer decides to investigate the effects of combinations of two temperatures (50 C and 60 C) and three stirring rates (60 rpm, 90 rpm, and 120 rpm) on the yield of the process. Ten batches of feedstock will be processed at each combination of temperature and stirring rate. 2. What are the experimental units? a) The two temperatures. b) The three stirring rates. c) The combinations of two temperatures and three stirring rates. d) The batches of feedstock e) The yield. 3. Identify the explanatory variable(s). a) The two temperatures. b) The three stirring rates. c) The combinations of two temperatures and three stirring rates. d) The batches of feedstock e) The yield. 4. What is the response variable(s). a) The two temperatures. b) The three stirring rates. c) The combinations of two temperatures and three stirring rates. d) The batches of feedstock e) The yield. 5. How many treatments are there? a) 2 b) 3 c) 5 d) 6
e) None of these
6. How many experimental units are needed? a) 2 b) 3 c) 5 d) 6 e) None of these
7. Which of the following in NOT a requirement of an experiment? a) control b) comparison c) replication d) randomization e) All of these above are required. 8. Which of the following statements is true? a) Age is often a confounding variable when measuring height of children. b) Case-control studies are the preferred type of observational study. c) Simple random samples are always the best way and only way to sample a population. d) All of the above are true. e) Exactly two of the above are true (excluding d). 9. Which of the following data collection methods could be used to poll students regarding political issues at a small community college? a) Simple random sample b) Systematic sampling c) Clustering d) All of the above are true e) Exactly two of the above are true (excluding d) 10. Randomization is necessary because… a) we want to eliminate (minimize) bias in the response bias. b) we want to control for the affect of confounding variables. c) we don’t want systematic errors in our outcomes. d) All of the above are true e) Exactly two of the above are true (excluding d) 11. Identical twins are separated at birth to study the affects of socio-economics and family stability has on behavioral development, this is an example of which of the following? a) Block b) Multi-stage c) Clustering d) Stratified e) Matched Pair 12. A high school has 35% freshmen, 30% sophomores, 25% juniors, and 10% seniors. If a random sample of 100 subjects was planned consisting of the same proportion of freshmen, sophomores, juniors and seniors, then this is an example of which of the following? a) Block b) Multi-stage c) Clustering d) Stratified e) Matched Pair
13. A survey is to be undertaken of recent nursing graduates in order to compare the starting salaries of women and men. For each graduate, three variables are to be recorded (sex, starting salary, and area of specialization). a) Sex AND starting salary are explanatory variables; area of specialization is a response variable. b) Sex is an explanatory variable; starting salary AND area of specialization are response variables. c) Sex is an explanatory variable; starting salary is a response variable; are of specialization is a possible confounding variable. d) Sex is a response variable; starting salary is an explanatory; area of specialization is a possible confounding variable. e) Sex AND area of specialization are explanatory variables; starting salary is a response variable. Twelve people who suffer from chronic fatigue syndrome volunteer to take part in an experiment to see if shark fin extract will increase one’s energy level. Eight of the volunteers are men and four are women. Half of the volunteers are to be given shark fin extract twice a day and the other half a placebo twice a day. We wish to make sure that four men and two women are assigned to each treatments, so we decide to use a block design with the men forming one block and the women the other. 14) A block design is appropriate in this experiment if a) we believe men and women will respond differently to treatments. b) gender equity is an important legal consideration in this study. c) we want the conclusions to apply equally to men and women. d) all of the above. 15) Suppose one of the researchers (not the doctor) is responsible for determining if a subject displays an increase in energy level. In this case, we should probably a) use two placebos. b) use stratified sampling to assign subjects to treatments. c) use fewer subjects but observe them more frequently. d) conduct the study as a double-blind experiment. 16) Which of the following is not a major principle of experimental design? a) control b) randomization c) replication d) segmentation A group of college students believes that herbal tea has remarkable restorative powers. To test their theory they make weekly visits to a local nursing home, visiting with residents, talking with them, and serving them herbal tea. After several weeks, many of the residents are more cheerful and healthy. 17) The explanatory variable in this experiment is a) the emotional state of the residents. b) the herbal tea. c) the fact that this is a local nursing home. d) the college students. 18) The response variable in this experiment is a) the emotional state of the residents. b) the herbal tea. c) the fact that this is a local nursing home. d) the college students.
19) The confounding variable in this experiment is a) the emotional state of the residents. b) the herbal tea. c) the fact that this is a local nursing home. d) the visits of the college students. 20) Two variables in a study are said to be confounded if a) one cannot separate their effects on a response variable. b) they are highly correlated. c) they do not have a normal distribution. d) one of them is a placebo. 21) Suppose volunteers were first divided into men and women, and then half the men were randomly assigned to a new drug treatment as were half of the women. The remaining volunteers were treated with a standard drug. This would be an example of a) replication. b) confounding. The effects of gender will be mixed up with the effects of the drugs. c) a block design. d) a matched-pair design. 22) Suppose volunteer were first divided into men and women. The volunteers were randomly treated with either the new drug or the standard depending on the outcome of a flip of a fair coin (heads-new, tails-standard). After three weeks, the volunteers were treated with the other treatment. a) replication. b) confounding. The effects of gender will be mixed up with the effects of the drugs. c) a block design. d) a matched-pair design. 23) A stratified random sample corresponds to which of the following experimental designs? a) a block design b) a double-blind experiment c) an experiment with a placebo d) a confounded, nonrandomized study
24) An education researcher randomly selects 40 high schools in Missouri and interviews all the teachers at each of the 40 high schools. Identify the type of sampling used in this example. a) Stratified sampling b) Attempted census c) Voluntary sampling d) Cluster sampling 25) At a small high school there are 120 freshmen, 90 sophomores, 110 juniors, and 80 seniors. A school administrator selects a random sample of 12 of the freshmen, a random sample of 9 out of the sophomores, a random sample of 11 of the juniors, and a random sample of 8 of the seniors. The administrator then interviews all the students selected. Identify the type of sampling used in this example. a) Stratified sampling b) Attempted census c) Voluntary sampling d) Cluster sampling
Observation vs. Experiment 26) At one hospital in 1992, 674 women were diagnosed with breast cancer. Five years later, 88% of the Caucasian women and 83% of the African American women were still alive. a) Observational Study b) Experimental Study 27) A researcher wished to assess the importance of exercise in weight-loss programs. 412 people, all considered to be at least 20 pounds overweight, volunteered to participate in a study. The participants were randomly assigned to one of two groups. Over a two-month period, the first groups followed a particular diet but were instructed to perform no exercise other than walking. The second group followed the same diet but also performed aerobic exercise for one hour each day. At the end of the two months, the weight loss of each participant was recorded. The average weight loss was calculated for each group and it was found that the average weight loss for the second group was significantly greater than the average weight loss for the first group. a) Observational Study b) Experimental Study Matching—identify the specified element in the experiment. In a clinical trial, 780 participants suffering from high blood pressure were randomly assigned to one of three groups. Over a one-month period, the first group received a low dosage of an experimental drug, the second group received a high dosage of the drug, and the third group received a placebo. The diastolic blood pressure of each participant was measured at the beginning and at the end of the period and the change in blood pressure was recorded. IDENTIFY 28) ____ Response variable measured. (A) The dosage of the drug 29) ____ Factor in the experiment. (B) The one-month period 30) ____ Levels in the factor. (C) The participants in the experiment 31) ____ Treatments. (D) Placebo, low dosage of drug, high dosage of drug (E) Low dosage of drug, high dosage of drug (F) Change in diastolic blood pressure (G) Diastolic blood pressure at start and end (H) High blood pressure, low blood pressure Can the following experiments be conducted using a single blind, double blind, or both. 32) Is the aspirin produced by a particular pharmaceutical company better than that of a competitor at relieving headaches? a) single blind b) double blind c) both 33) Only the researchers (statisticians) know which group of participants is receiving a placebo? a) single blind b) double blind c) both
FREE RESPONSE Turkeys raised commercially for food are often fed the antibiotic salinomycin to prevent infections from spreading among the birds. However, salinomycin can damage the birds’ internal organs, especially the pancreas. A researcher believes that a combination of effects of two different dosages of selenium (call them S1 and S2) in combination with any of three different dosages of vitamin E (call them E1, E2, and E3) added to the turkeys’ diets. There are 48 turkeys available for the study. At the end of the study, the birds will be killed and the condition of their pancreas examined with a microscope. 34. Describe (in detail) an appropriate design for this experiment.
Brief Article: Aspirin May Enhance Impairment of Alcohol Aspirin, a longtime antidote for the side effects of drinking, may actually enhance alcohol’s effect, researchers at the Bronx Veteran’s Affairs Medical Center say. In a report on a study published in the Journal of the American Medical Association, the researchers said they found that aspirin significantly lowered the body’s ability to break down alcohol in the stomach. As a result, five volunteers who had a standard breakfast and two extra-strength aspirin tablets an hour before drinking had blood levels 30 percent higher than when they drank alcohol alone. Each volunteer consumed the equivalent of a glass and a half of wine. That 30 percent could make a difference between sobriety and impairment, said Dr. Charles S. Lieber, medical director of the Alcohol Research and Treatment Center at the Bronx center, who was co-author of the report with Dr. Risto Roine. 35. Does this article describe an experiment? Explain. Yes, this article describes an experiment. The study imposed a treatment (took aspirin before drinking alcohol). Imposing a treatment is what makes a study an experiment so this is an experiment. 36. Did this study involve a simple random sample (SRS)? No, this study did not involve a simple random sample because the participants are volunteers. There were not randomly selected and therefore are not an SRS. 37. Did this study use a particular design that we have studied? If so, identify the design. THEN comment on the validity of the study. This study is a matched-pairs design because the study compared the blood alcohol levels of a single individual after taking aspirin and without taking aspirin. There are many concerns I have about the validity of the study. There are only 5 subjects and they are all volunteers and therefore not representative of the population.
38. Suppose that a sample of adults in a community is selected using a random digit dialing from a telephone directory. Explain why or why not this sample would be representative of the population of interest. This is not representative of the population because people with cell phones only (no landlines) and homeless people are not represented in this sample.
39. A high school has 200 A students, 300 B students, 400 C students, 200 D students, and 100 F students. Some students are to randomly selected to respond to a survey. a) Describe a stratified random sampling method in which each student by letter category (grade) has a 10% chance of being selected. Randomly select 20 A students, 30 B students, 40 C students, 20 D students, and 10 F students to respond to the survey. b) Describe a simple random sampling method in which 120 students are selected. Randomly select 120 students from the entire population of the 1200 students ignoring their letter category and ask them to respond to a survey.
40. Pantherentrum is a new wonder drug that prevents students from skipping classes. Explain how researchers could conduct a double-blind experiment to compare Pantherentrum chewable pills in preventing skip-aridous. To conduct a double-blind experiment, researchers must label the appropriate pills (Pantherentrum or placebo) for each student. The identical looking medication will be distributed by nurses to the students. Only the researchers will know who is taking each pill. The nurses and the students will not know.
41. List and describe all types of sampling bias. Undercoverage Non-Response Bias Response Bias Wording Effects
42. (1997 #2) A new type of fish food has become available for catfish raised on fish farms. Your task is to design an experiment to compare the weight gain of catfish raised over a six-month period on the new and old types of food. The catfish you will use for this experiment have already been randomly placed in the eight tanks in a big room that has a considerable temperature gradient. Specifically, tanks on the north side of the room tend to be much cooler than those on the south side. The arrangement of tanks is shown on the diagram below. The tanks, windows, door, and heater are not moveable. The catfish must stay in their pre-
assigned randomly selected tanks. Describe a design for this experiment that takes account of the temperature gradient.
43. (2001 #4) Students are designing an experiment to compare the productivity of two varieties of dwarf fruit trees. The site for the experiment is a field that is bordered by a densely forested area on the west (left) side. The field has been divided into eight plots of approximately the same area. The students have decided that the test plots should be blocked. Four trees, two of each of the two varieties, will be assigned at random to the four plots within each block, with one tree planted in each plot.
The two blocking schemes shown below are under consideration. For each scheme, one block is indicated by the white region and the other block is indicated by the gray region in the figures.
(a) (b)
Which of the blocking scheme, A or B, is better for this experiment? Explain your answer. Even though the students have decided to block, they must randomly assign the varieties of trees to the plots within each block. What is the purpose of this randomization in the context of this experiment?
