Chapter 5 Review. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

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1 Class: Date: Chapter 5 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The Women s Health Study randomly assigned nearly 40,000 women over the age of 45 to receive either aspirin or a placebo for over 10 years to examine the effect of aspirin on cancer risk to healthy women. This long-term trial was best conducted as a. a census b. an observational study c. a randomized comparative experiment d. a single-blind randomized comparative experiment e. a double-blind randomized comparative experiment 2. In the previous problem, suppose that the researchers suspected that women over the age of 55 may respond differently to the treatment. Given that a random sample of 40,000 women over the age of 45 has already been chosen, the study would have been improved by a. a stratified sample, with strata determined by age b. a stratified sample, with strata by gender c. a block design, with blocks determined by age d. a block design, with blocks determined by gender e. a double-blind completely randomized design 3. Researchers were interested to know whether internal vehicle temperatures vary by outside temperatures. To evaluate this, temperature rise was measured continuously over a 60-minute period in a dark sedan on 16 different clear, sunny days outside with temperatures ranging from 72º F to 96º F. The researchers method of analysis is best described as a. a census b. a survey c. an observational study d. a randomized comparative experiment e. a single-blind randomized comparative experiment 4. Respondents to a randomly distributed questionnaire answered the questions, Do you agree that nuclear weapons should never be used because they are immoral? The study that uses the results of this questionnaire will most likely suffer from which type of bias? a. undercoverage b. voluntary response c. response d. nonresponse e. all of the above 5. A statistics teacher decided to compare this year s students to all those she has taught over the history of the course. She will use the students s examination performances as the method of comparison. Which of the following is true in this context? a. The mean performance of this year s students is a parameter b. The mean performance of this year s students is a statistic c. The mean of all except this year s students is a parameter d. The mean of all students is a statistic e. None of these is true 1

2 Use the information below for the next three questions. Left-handedness is the preference for the left hand over the right for everyday activities such as writing. Studies indicate that about 93% of the population may be characterized as right-handed. Researchers would like to conduct a study to determine if left-handed teens differ significantly in their ability to memorize facts rather than right-handed teens. 6. The explanatory variable in this study is a. ability to memorize facts b. age c. handedness d. researchers e. none of the above 7. A random-number table is used to simulate the number of teens selected before a left-hand teen is found. A proper assignment of digits is a. let the digits 0-6 represent a left-handed teen and 7-99 represent a right-handed teen; ignore repeats of numbers 7-99 until you get a number from 0-6 b. let the digits 0-6 represent a left-handed teen and 7-99 represent a right-handed teen; ; count repeats of numbers 7-99 and continue until you get a number from 0-6 c. let the digits represent a left-handed teen and represent a right-handed teen; ignore repeats of numbers until you get a number from d. let the digits represent a left-handed teen and represent a right-handed teen; count repeats of numbers and continue until you get a number from e. let the digits represent a left-handed teen and represent a right-handed teen; count repeats of numbers and continue until you get a number from Suppose the researchers concluded that the average number of words memorized by left-handed teens was statistically significantly higher than the average number memorized by right-handed teens. In this context, statistically significant means that a. the number of words memorized by left-handed teens exceeded the number of words memorized by right-handed teens b. the average number of words memorized by left-handed students exceeded the average number of words memorized by right-handed students c. right-handed students tend to not do as well as left-handed students in memorizing d. it would be unlikely to observe an average difference as large as was observed by chance variation e. a randomized, controlled, experiment was conducted 9. Pollsters are interested in conducting a survey to determine if students who belonged to an online social network during college continued with it after graduation. They plan to randomly select 50 people from a list of registered voters. A problem with the proposed plan is that the a. sampling frame may be different from the population of interest b. sample size is too small c. sample is a systematic random sample d. sample was not stratified by political party e. sampling design should incorporate multistage sampling 2

3 10. The purpose of randomization in an experiment is to a. make the experiment seem fair b. make the treatment groups as similar as possible c. make the treatment groups as different as possible d. create blocks on an experiment e. reduce variability within treatment groups 11. Ben conducts a study in which 100 subjects, randomly chosen from the population of all students at a high school, guess when 60 seconds have elapsed. He records the actual number of seconds that have elapsed when the subject thinks it has been 60 seconds. The subjects make their guesses while listening to music. They have a choice of two treatments, fast music or slow music. Fifty-five of Ben s subjects choose fast music and 45 choose slow music. What kind of study is this? a. Experiment, because the subjects are responding to treatments b. Experiment, because there is a response variable c. Experiment, because the subjects are randomly chosen from the population d. Observational study, because the participants select their own music e. Observational study, because the treatment groups are different sizes 12. Which of the following statements about observational studies are true? I. A census is always preferable to a sample survey since it includes the entire population II. A neutral designer of a survey who has no predisposition towards any particular conclusion can still produce biased data III. Statistical inference is not necessary when a census is conducted properly a. I only b. II only c. I and II d. I and III e. II and III 13. A consumer investigative agency wants to determine how gas mileage varies for a particular type of car under different driving conditions and using different grades of fuel. For the experiment, 120 cars of this type are available. Experimental trials will be conducted using two driving conditions: stop-and-go city driving, and high-speed highway driving. The trials will also use three fuel grades: regular, plus, and premium. All possible combinations of these driving conditions and fuel grades will be used in this experiment, and the cars will be randomly assigned to treatment groups. Which of the following properly describes the factors, levels, and/or treatments in this experiment? a. There are 2 factors, one with 2 levels and one with 3 levels b. There are 2 factors and 5 treatments c. There are 2 factors and 6 levels d. There are 5 factors and 6 treatments e. There are 5 factors and 120 treatments 14. A U.S. government researcher wants to select a sample of tax returns that will include returns from a variety of different income levels. He divides the set of all the different incomes shown on the forms into 10 nonoverlapping ranges, then he randomly selects 100 tax returns from each. Which of the following best describes the sampling scheme used in this example? a. Stratified random sampling b. Simple random sampling c. Convenience sampling d. Two-stage sampling e. Cluster sampling 3

4 15. Which of the following is NOT a property of a large table of random digits? a. The table will contain, somewhere, the sequence of digits 1234 b. Consecutive rows do not start with the same digit c. Each digit 0 through 9 occurs with equal frequency d. Each three-digit number 000 through 999 occurs with equal frequency e. The contents of one section of the table are independent of other sections of the table 16. The owner of a factory that employs half the citizens in a small town is trying to decide whether to take a public stand on a controversial issue. He realizes that he would benefit from knowing how the townspeople feel. He randomly selects 50 of the townspeople from a list of all the town s population. He personally contacts all 50 and asks them their opinion on the issue. Most give him an answer, but 12 townspeople decline to participate. He decides to summarize his results based in the 38 responses. Which of the following lists the most significant sources of bias in this survey? a. Voluntary response bias and undercoverage b. Response bias and undercoverage c. Nonresponse and undercoverage d. Response bias and nonresponse e. Voluntary response bias and nonresponse 17. A researcher is trying to find the best soil composition for growing a new variety of tomato. The researcher is considering 4 different soil nutrients, each with 5 possible levels. A large field is split into different plots, one for each possible combination of nutrients level. The placement of each combination is random. The researcher plants one tomato plant in each plot, and the success of each nutrient combination will be measured by the size of the tomatoes produced by each plant. Which of the following is the most serious problem with this design? a. Lack of replication b. Lack of control c. Lack of randomization d. The experiment isn t double blinded e. Placebo effect 18. Which of the following is the least important way in which the designer of an experiment can guard against confounding variables? a. Matching b. Randomization c. Replication d. Control e. Blocking 19. David knows that dancers are trained to spin many times without losing ability to move in a straight line after spinning. He wonders whether this ability is dependent on the number of spins. He wants to design an experiment that will compare the ability of experienced female dancers to walk a fixed distance in a straight line after 5 spins with their ability after 10 spins. Which of the following is the most appropriate design for this experiment? a. Completely randomized design b. Stratified design c. Randomized block design d. Cluster design e. Matched pairs design 4

5 20. High cholesterol levels can lead to heart disease and other health problems. A new medicine is being introduced to lower cholesterol levels, but it is suspected of harming the livers of some patients. A study is conducted on 244 patients with high cholesterol. The group subjects are randomly assigned to two treatment groups with 122 subjects in each group. One group is given the new medicine, and the other was given a placebo. After two years, the study showed more liver problems among the group given the new medicine. Which of the following statements about the generalizability of the study is best supported by these results? a. Cholesterol is harmful to a person s health, so it is worth risking liver problems in order to reduce it b. The experiment demonstrates that the new medicine causes an increase in liver problems c. This is an observational study, so no conclusion can be drawn about cause-and-effect d. It is not clear whether the difference in liver problems is statistically significant, so no conclusion can be drawn e. Two years is too short of a time for the experiment, so no conclusion can be drawn 21. Which of these best explains why large samples tend to prove more reliable inference about a population than small samples? a. The response variable will be measured more effectively b. There is a smaller probability of bias c. It will be less of a problem if the randomization is imperfect d. Large samples are more diverse e. Large samples show less sampling variability 22. An opinion survey is going to be conducted at two colleges. College A has 5000 students and College B has 20,000 students. Each survey will be conducted with a simple random sample of 200 students. The results from each survey will be used as an estimate for the opinions of the student body at each college. Which college is likely to have its students opinions estimated more accurately by the survey? a. College A since it has a larger percentage of its students surveyed b. College A since the larger school is likely to have more diversity of opinion c. Neither college is more likely to have a more accurate estimate d. College B since the students with out-of-the-mainstream opinions will have less of an influence on the average student opinion at a larger school e. College B since there is less sampling variability with a larger sample 23. A school committee is lobbying for an increase in the gasoline tax to support the county school system. The local newspaper conducted a survey of county residents to assess their support for such an increase. What is the population of interest here? a. All school-aged children b. All county residents c. All county residents with school-aged children d. All county residents with children in the county school system e. All county school system teachers 24. A manufacturer of ready-bake cake mixes is interested in designing an experiment to taste the effects of four different temperature levels (300º, 325º, 350º, and 375º), two different types of pans (glass and metal), and three different types of ovens (gas, electric, and microwave) on the texture of its cakes, in all combinations. Which of the following below has the best description of the design of the necessary experiment? a. A completely randomized design with nine treatments b. A completely randomized design with twenty-four treatments c. A randomized block design, blocked on temperature with six treatments d. A randomized block design, blocked on type of pan, with twelve treatments e. A randomized block design, blocked on type of oven, with eight treatment groups 5

6 25. An experiment was designed to test the effects of 3 different types of paint on the durability of wooden toys. Because boys and girls tend to play differently with toys, a randomly selected group of children was divided into two groups by sex. Which of the following statements about this experiment is true? a. There are three types of paint and 2 sex groups, giving a total of 6 combinations in this experiment b. Type of paint is a blocking factor c. Sex is a blocking factor d. This is a completely randomized design e. This is a matched-pairs design in which one boy and one girl are matched by age to form a pair 26. In a clinical trial, 30 sickle cell anemia patients are randomly assigned to two groups. One group receives the currently marketed medicine, and the other group receives an experimental medicine. Each week, patients report to the clinic where blood tests are conducted. The lab technician is unaware of the kind of medicine the patient is taking. The design can be described as a. a completely randomized design, with the currently marketed medicine and the experimental medicine as two treatments b. a matched-pair design, with the currently markets medicine and the experimental medicine forming a pair c. a randomized block design, with the currently marketed medicine and the experimental medicine as two blocks d. a randomized block design, with the currently marketed medicine and the experimental medicine as two treatments e. a stratified design with two strata, patients with sickle cell disease forming one stratum and those without sickle cell disease forming the other stratum 27. A newspaper reporter examined police reports of accidents during the past 12 months to collect data about the speed of a car and its stopping distance. The reporter then constructed a scatterplot and computed a correlation coefficient to show the relation between a car s speed and it stopping distance. This is an example of a. a double-blind study b. a single-blind study c. a study involving no blinding at all d. an observational study e. a well-designed experiment 28. A company with offices in five different countries is interested in estimating the proportion of its employees in favor of banning smoking on the office premises. It is known that the views of people from different countries on issues like smoking tend to vary due to the influence of different local social structures. Which of the following is an appropriate sampling technique to use in this situation, and why? a. Stratified sample, because the population is divided into five strata-namely, five offices in five different countries b. Cluster sample, because the population is divided into five clusters-namely five office in five different countries c. Simple random sample, because this is the simplest sampling method d. Simple random sample, because this is the only method that gives unbiased results e. Simple random sample, because this is the only method for which inferential techniques are available 6

7 29. In a clinic, 50 patients with sleep disorders are randomly assigned to one of two different groups. Patients in one group are given medication before bedtime. Patients in the other group are given blindfolds and played soft music at bedtime. Each patient is attached to a machine that records breathing patterns. From the patterns, it is possible to determine if the patient is awake or asleep. The data will be used to decide which method is more effective in helping patients with sleep disorders. Which of the following statements is correct in the context of this experiment? a. It is not possible for this experiment to be single-blind or double-blind, because human subjects are involved b. This is only a single-blind experiment because the experiments did not include a control group that received neither medication nor a blindfold and soft music c. This is only a single-blind experiment because patients will know which treatment they are receiving, although the examining doctor might not d. This is a double-blind experiment because the experimenters could prevent both groups of patients from knowing what sort of treatment the other group is receiving e. This is a double-blind experiment because the patients were divided into two treatment groups randomly 30. Each of the 30 major league baseball teams carries a 40-person roster. A sample of 60 players (5 percent of all 1,200 players) is to be randomly selected to undergo drug tests. To do this, each team is instructed to put their 40 names in a hat and randomly draw two names. Will this method result in a simple random sample? a. Yes, because each player has the same chance of being selected b. Yes, because each team is equally represented c. Yes, because this is an example of stratified sampling, which is a special case of simple random sampling d. No, because the teams are not chosen randomly e. No, because not each group of 60 players has the same chance of being selected Short Answer 31. A political party s position on a ballot is often determined by random selection. For the last 10 years, the Innovators have never had the coveted position on the ballot; this position has gone to either Old-Timers or Preservationists. The Innovators have cried foul. Use the random-number table below to test the likelihood of the disputed result. Clearly communicate your scheme, conduct 10 trials, and report your results Researchers at a company that manufactures health and beauty products are working on a new foot lotion formula for women with extremely dry feet. They plan to test the new formula against their current product. Fifty women with extremely dry feet have been identified and have volunteered to participate in a clinical trial over a period of 6 months. An experimental design considered by researchers is to divide the volunteers into two equal groups, one which will use the new formula for the first 3 months and then use the current product. The other group will use the current formula first and then use the new formula. The experiment is to be double-blind. At the end of each 3-month period, the researchers will measure foot dryness and will compare the results of the two treatments at the end of the trial. Propose an alternative design and explain why your design is better. 7

8 33. An experiment concluded that low-dose aspirin is an effective treatment to prevent heart attacks in men who have already experienced and survived one heart attack. In the experiment, 1000 volunteers were randomly assigned to one of two treatment groups. One group took a low-dose aspirin every day, and the other group took a pill that looked exactly like the aspirin pill but contained no medicine. The subjects were given treatment over a three-year period. The experimenters then determined how many in each group suffered a second heart attack over this period. The experimental evidence for the effectiveness of the aspirin treatment was so convincing that all the participants were put on the low-dose aspirin regimen at the end of the experiment. a) What measures in this experimental design ensure that the collection of data is not haphazard? b) Describe the explanatory and response variables in the experiment. c) If there was no second group and all of the subjects had been given the low-dose aspirin, would this still be an experiment? 34. Administrators at a high school hire an independent research firm to conduct a survey of the high school s alumni to find out how satisfied they are with their education at the school. Once or twice a year, the high school contacts alumni in order to keep records of current contact information. The research firm selects its sample from a list of alumni who have responded to the school s communications and have provided current contact information. a) Point out a potential source of bias, and how you believe that source of bias will affect the survey s ability to estimate the level of satisfaction for all alumni. b) The research firm wants to make sure that separate results are available for alumni who have graduated in the last 10 years, 11 to 20 years ago, and 21 or more years ago. Describe a sampling method that will meet this requirement. 35. Product testers for a carpet manufacturer want to discover which of two brands of stain proofing chemicals, A or B, is more effective at combating routine wear and tear when used on the company s carpets. An experiment is to be designed to decide which brand to use. The testers believe, however, that two different carpet types made by the company, berber and cut pile, might not respond the same to the two types of stain proofing. There are 200 berber and 200 cut pile samples, all the same color, available for testing. After treatment with stain proofing, the product testers will subject all samples to a simulation of one year s wear and tear. The effectiveness of the stain proofing will be measured by digital imaging techniques that measure the color change in the samples. a) Design a randomized block design for this experiment that will allow the product testers to decide the best design to use for each type of carpet. b) Replication is a part of this experiment. Describe replication taking place here, and explain why it is important. 8

9 36. Claire is investigating whether gender is a factor in the relationship between the memorizing skills of third grade students and the same students belief in their memorizing skills. Claire performs a study with a large sample of 8-year-old children, equally split between boys and girls. Assume this is a representative sample of the population of all 8-year-old boys and girls in the United States. She tells them that they will be given a list of 20 nonsense words and that they will have 5 minutes to memorize as many words as they can. Then they will be given 5 minutes to write down as many of the words as they can remember in any order they like. Before she shows them the list, she asks each of them to write down the number of words they expect they will get right. She then has them go through the memorization and recall steps. Then she computes, for each child, the actual number of word right minus the predicted number of words right. Then she computes the mean of these values for boys and the mean for girls. Claire finds that this mean difference is larger for girls than it is for boys. a) What does this result tell you about the sample? b) If Claire s result about the comparison of mean differences is statistically significant, does this prove than gender is the cause of the discrepancy in performance for the population of interest? 37. Salmon farmers have a choice of three different types of food (type A, type B, and type C) and two different breeds (Sockeye and Chinook). The salmon farmers want you to design an experiment in which you feed the different types of food to the two breeds of salmon to see which type of food leads to the largest salmon. They provide you with sixty salmon divided equally between the two breeds and can provide you with up to ten different tanks in which to raise the salmon. The farmers would like the results in ten weeks. a) Design an appropriate experiment b) Is your design single-blind, double-blind, or neither. Explain. 9

10 38. 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 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 regions and the other block is indicated by the gray region in the figures. a) Which of the blocking schemes, A or B, is better for this experiment? Explain your answer. b) 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? 10

11 39. A preliminary study conducted at a medical center in St. Louis has shown that treatment with small, low-intensity magnets reduces the self-reported level of pain in polio patients. During each session, a patient rested on an examining table in the doctor s office while the magnets, embedded in soft pads, were strapped to the body at the site of pain. Sessions continued for several weeks, after which pain reduction was measured. A new study is being designed to investigate whether magnets also reduce pain in patients suffering from herniated disks in the lower back. One hundred male patients are available for the new study. a) Describe an appropriate design for the new study. Your discussion should briefly address treatments used, methods of treatment assignment, and what variables would be measured. Do not describe how the data would be analyzed. b) Would you modify the design above, if instead of 100 male patients, there were 50 male and 50 female patients available for the study? If so, how would you modify your design? If not, why not? 40. In search of a mosquito repellent that is safer than the ones that are currently on the market, scientists have developed a new compound that is rated as less toxic than the current compound, thus making a repellent that contains this new compound safer for human use. Scientists also believe that a repellent containing the new compound will be more effective than the ones that contain the current compound. To test the effectiveness of the new compound versus that of the current compound, scientists have randomly selected 100 people from a state. Up to 100 bins, with an equal number of mosquitoes in each bin, are available for use in this study. After a compound is applied to a participant s forearm, the participant will insert his or her forearm into a bin for 1 minute, and the number of mosquito bites on the arm at the end of the time will be determined. a) Suppose this study is to be conducted using a completely randomized design. Describe a randomization process. b) Suppose this study is to be conducted using a matched pair design. Describe a randomization process. c) Which of the designs, the one in part (a) or the one in part (b), is better for testing the effectiveness of the new compound versus that of the current compound? Justify your answer. 11

12 41. When a tractor pulls a plow through an agricultural field, the energy needed to pull that plow is called the draft. The draft is affected by environmental conditions such as soil type, terrain, and moisture. A study was conducted to determine whether a newly developed hitch would be able to reduce draft compared to the standard hitch. (A hitch is used to connect the plow to the tractor.) Two large plots of land were used in this study. It was randomly determined which plot was to be plowed using a standard hitch. As the tractor plowed that plot, a measurement device on the tractor automatically recorded the draft at 25 randomly selected points in the plot. After the plot was plowed, the hitch was changed from the standard one to the new one, a process that takes a substantial amount of time. Then the second plot was plowed using the new hitch. Twenty-five measurements of draft were also recorded at randomly selected points in this plot. a) What was the response variable in this study? Identify the treatments. What were the experimental units? b) Given the goal of the study is to determine whether a newly developed hitch reduces draft compared to the standard hitch, was randomization used properly in this study? Justify your answer. c) Given that the goal of the study is to determine whether a new developed hitch reduces draft compared to the standard hitch, was replication used properly in this study? Justify your answer. d) Plot of land is a confounding variable in this experiment. Explain why. 12