INSTANT DOWNLOAD WITH ANSWERS
MIND ON STATISTICS 5TH EDITION BY UTTS – TEST BANK
Mind on Statistics Test Bank
Chapter 6
Section 6.1
Questions 1 to 10: Decide if the study is an observational study or an experiment.
- Twenty blue-fin tuna were randomly assigned to two tanks of water, 10 tuna in each tank. One tank was polluted with methyl mercury, while the other tank was not polluted. The survival times of the fish in the two tanks were compared.
- Observational Study
- Experiment
KEY: B
- A biologist measured the increasing amounts of phosphorus in Lake Erie and observed a decreasing number of lake trout over a 5-year period.
- Observational Study
- Experiment
KEY: A
- A study compared the IQ from children whose mothers smoked to the IQ from children whose mothers didn’t smoke.
- Observational Study
- Experiment
KEY: A
- Thirty-six students were randomly assigned to listen to Mozart (18 students) or a relaxation tape (18 students). The IQ of the students were measured afterwards.
- Observational Study
- Experiment
KEY: B
- A medicine to remove the redness in eyes was tested in a group of 100 students. Each student took the medicine in one eye and a placebo in the other eye. The eye (left or right) that received the placebo was decided by flipping a coin.
- Observational Study
- Experiment
KEY: B
- A study compared a group of men who had heart attacks with a similar group of controls. The proportion of men with male pattern baldness was compared between the two groups.
- Observational Study
- Experiment
KEY: A
- 100 students were followed over a 6-month period. The number of students who took Echinacea (a herbal supplement) and the number who developed colds were recorded.
- Observational Study
- Experiment
KEY: A
- A sample survey of 100 voters was used to compare the proportion of women in the Democratic and Republican parties.
- Observational Study
- Experiment
KEY: A
- To investigate how trans fat consumption might affect fertility, researchers analyzed data available from 18,555 healthy women who participated in the Nurses’ Health Study between 1991 and 1999.
- Observational Study
- Experiment
KEY: A
- One hundred adults who had either Type 1 or Type 2 diabetes were randomly divided into 2 groups to determine if the inhalable version of insulin is able to manage blood sugar levels just as well as injected insulin.
- Observational Study
- Experiment
KEY: B
Questions 11 to 13: A researcher asked random samples of 50 kindergarten teachers and 50 12th grade teachers how much of their own money they spent on school supplies in the previous school year. They wanted to see if teachers at one grade level spend more than teachers at the other grade level.
- In this study, the grade level taught (kindergarten or 12th grade) is an example of
- a randomly assigned treatment.
- an explanatory variable.
- a response variable.
- a normal variable.
KEY: B
- In this study, the reply to the question about amount spent on school supplies is an example of
- a randomly assigned treatment.
- an explanatory variable.
- a response variable.
- a normal variable.
KEY: C
- In this study, it turns out that 12^{th} grade teachers generally earn more money than kindergarten teachers. The variable ‘income of the teacher’ is an example of
- a dependent variable.
- a confounding variable.
- a response variable.
- a normal variable.
KEY: B
- A researcher conducts a study to determine whether or not taking Vitamin C prevents colds. What is the explanatory variable in this study?
- Whether or not one takes Vitamin C.
- Whether or not one gets colds.
- Whether or not one is a participant in the study.
- Whether or not one knows which treatment one is taking.
KEY: A
- In an observational study, confounding means
- having more than one response variable.
- that the effect of the explanatory variable on the response variable changes for different categories of a third variable.
- that the effects of several variables are tested at one time.
- that the effect of the explanatory variable on the response variable can’t be separated from the effect of other variables on the response.
KEY: D
- Which of the following is true about confounding variables in observational studies?
- If a confounding variable is present, then we know that a change in the explanatory variable cannot cause a change in the response variable.
- If a confounding variable is present, it is possible that a change in the explanatory variable causes a change in the response variable, but it is hard to separate the effect of the explanatory variable and the effect of the confounding variable on the response.
- Confounding variables are not a problem in observational studies because we only observe the explanatory and response variables.
- Confounding variables are only a problem in observational studies if they are also interacting variables.
KEY: B
- A study was conducted to compare the grade point averages (GPAs) of male and female students majoring in Psychology. In this study
- gender and GPA are both response variables.
- gender and GPA are both explanatory variables.
- GPA is an explanatory variable and Gender is a response variable.
- gender is an explanatory variable and GPA is a response variable.
KEY: D
- A medical doctor is comparing two treatments for high cholesterol. She puts the names of 40 patients with high cholesterol into a box, and randomly draws the names of 20 patients. These 20 patients are given treatment 1. The doctor gives treatment 2 to the remaining 20 patients. What type of study design is this?
- Observational study
- Sample survey
- Randomized experiment
- Significant
KEY: C
Questions 19 to 20: Research is done to see whether taking oral contraceptives increases women’s blood pressures. The blood pressures of women who take oral contraceptives are compared to the blood pressures of women who do not take oral contraceptive. A complicating factor is that the women who take oral contraceptives tend to be younger than the others. This must be taken into account because blood pressure increases with age.
- Which variable is the response variable in this study?
- Age
- Blood pressure
- Oral contraceptive use
- Both age and oral contraceptive use are response variables in this study.
KEY: B
- Which variable is a confounding variable in this study?
- Age
- Blood pressure
- Oral contraceptive use
- There are no confounding variables in this study.
KEY: A
- An experiment is usually preferred to an observational study because
- one can draw a cause and effect conclusion in an experiment but not in an observational study.
- it is easier to collect data from an experiment than it is from an observational study.
- it is cheaper to run an experiment than it is to do an observational study.
- volunteers can be used for an experiment but not for an observational study.
KEY: A
- An observational study is done to see if eating at least two apples a week helps prevent tooth decay in children. However, the researchers are aware that children who eat apples may also drink less soda, so they measure soda consumption as well. In this example, soda consumption is an example of
- an interacting variable.
- an explanatory variable.
- a response variable.
- a confounding variable.
KEY: D
Questions 23 to 30: For each relationship (conclusions from one or more studies), define what the response and explanatory variables are.
- The average life expectancy in Russia dropped from 64 years (1991) to 57 years (1995). One theory was that radiation from nuclear fallout was responsible.
KEY: Response: Life expectancy; Explanatory: Radiation from nuclear fallout.
- Children who take the time to eat breakfast get higher grades in school than children who don’t eat breakfast.
KEY: Response: Grades in school; Explanatory: Eating breakfast
- The oldest child in a family is more likely to favor the death penalty than the middle or youngest child.
KEY: Response: Favoring the death penalty; Explanatory: Birth order (oldest child in the family).
- Second hand smoke (passive smoke) is a risk factor for chronic lung disease.
KEY: Response: Chronic lung disease; Explanatory: Second hand smoke.
- Listening to Mozart raised non-verbal IQ scores an average of 8 to 9 points higher than listening to relaxation tapes.
KEY: Response: Non-verbal IQ scores; Explanatory: Playing Mozart or a relaxation tape.
- College instructors with a Ph.D. degree earn, on average, more than college instructors with only a Master’s degree.
KEY: Response: Income; Explanatory: Education (Master or PhD.)
- Course grades based on student evaluations varied across the various fields. Social science courses generally received higher scores than natural science courses.
KEY: Response: Course grades from the student evaluations; Explanatory: Field of study (social science or natural science).
- Drinking as little as two cups of coffee before exercising limits the blood flow to the heart. An experiment with 18 young adults showed that when the subject remained inactive, the caffeine had very little affect, but after the subject participated in exercise, the caffeine slowed down the blood flow to the heart.
KEY: Response: Presence of slowing down of blood flow; Explanatory: Activity of subject (inactive or exercise).
Section 6.2
- Which of the following methods is not a good randomization procedure?
- Using a computer to generate a list of random numbers.
- Using a table of random numbers.
- Flipping a coin.
- Asking someone to pick numbers randomly between 1 and 10.
KEY: D
- The purpose of having a control group in a study is
- to estimate the response when the treatment is not applied.
- to decrease the margin of error.
- to be able to blind the subjects.
- to make the samples more representative.
KEY: A
- Eighty individuals who wished to lose weight were randomly divided into two groups of 40. One group was given an exercise program to follow while the other group was given a special diet. After three months, the researcher compared mean weight losses in the two groups. What type of study is this?
- Observational study
- Repeated measures study
- Matched pairs study
- Randomized experiment
KEY: D
Questions 34 to 36: Sickle-cell disease is a painful disorder of the red blood cells that in the United States affects mostly blacks. To investigate whether drug A can reduce the pain associated with sickle-cell disease, a study by the National Institutes of Health randomly assigned 150 sickle-cell sufferers to receive the drug. Placebos were given to another 150 sickle-cell sufferers. Great care was used to ensure that the 300 participants did not know if their pill contained the drug. At the end of the treatment period, the researchers counted the number of episodes of pain reported by each subject.
- What type of study is this?
- Observational study
- Randomized experiment
- Matched pairs study
- Repeated measures study
KEY: B
- What is the response variable in this study?
- Sickle-cell disease status (yes or no).
- Form of drug (pill or liquid).
- The number of episodes of pain.
- The number of red blood cells.
KEY: C
- Which of the following principles was not used in this study?
- Control
- Blinding
- Randomization
- Blocking
KEY: D
Questions 37 to 39: A researcher is studying the relationship between sugar consumption and weight gain. Twelve volunteers were randomly assigned to one of two groups. The first group had five participants which were put on a diet low in sugar and the other group with the remaining seven participants received 10% of their calories from sugar. After 8 weeks, weight gain was recorded from each participant.
- Which variable is the response variable in this study?
- Sugar consumption
- Diet low in sugar
- Weight
- Weight gain
KEY: D
- Which of the following principles was not used in this study?
- Repeated measures
- Blinding
- Randomization
- Control
KEY: B
- The ‘low sugar’ group can be thought of as a control group. The control group is being used in this experiment to avoid
- Confounding with the ‘10% sugar’ group
- Placebo effect
- Nonresponse bias
- Replication
KEY: B
Questions 40 to 42: Fifty university students are randomly chosen from the college campus. Their physical fitness routines and academic performance will be assessed. They are asked to maintain a diary over a semester to record their physical activity (i.e. work-outs) every week. At the end of this semester their GPA is recorded as well. The resulting information is categorized per student into two variables: physical activity (recorded as “above average”, “average”, or “below average”) and that semester’s GPA. The primary interest of the research project is to understand if physical activity promotes better academic performance.
- What type of study is this?
- Observational study
- Randomized experiment
- Matched pairs study
- Repeated measures study
KEY: A
- Which of the following principles was used in this study?
- Randomization
- Control
- Replication
- Blinding
KEY: C
- Which variable is the explanatory variable in this study?
- The diary
- Physical activity
- GPA
- Academic performance
KEY: B
Questions 43 to 45: Having a coffee fix just before a workout may not be the best idea, a study suggests. Researchers in Switzerland found that the amount of caffeine in just two cups of coffee limits the body’s ability to increase blood flow to the heart during exercise. The study included 18 young, healthy people who were regular coffee drinkers. They did not drink any coffee for 36 hours prior to study testing. The researchers used high-tech PET scans to measure the participants’ heart blood flow before and after they rode a stationary bike and then repeated the testing procedure after swallowing a tablet containing 200 milligrams of caffeine — the amount contained in two cups of coffee. The caffeine did not affect heart blood flow when the participants were inactive. However, measurements taken immediately after exercise showed a slowdown in heart blood flow after they’d taken the caffeine tablets, compared to their previous results.
- What type of study is this?
- Observational study
- Randomized block design
- Matched pairs study
- Repeated measures study
KEY: D
- Which variable is an explanatory variable in this study?
- The health of the participants
- Taking a caffeine tablet (yes or no)
- Difference in heart blood flow
- The PET scan
KEY: B
- Which variable is the response variable in this study?
- Caffeine content
- Physical activity (stationary bike)
- Difference in heart blood flow
- Taking a caffeine tablet (yes or no)
KEY: C
Questions 46 and 47: You wish to study the effect of a tutoring program to help improve student grades in an introductory statistics course.
- Propose an experimental study design to answer the question.
KEY: Randomly assign half the students in the class to take the tutoring program and the other half not to take the program. Compare the grades between the two groups.
- Propose a matched-pairs study design to answer the question.
KEY: Match students with a partner with a similar background in mathematics or statistics, and randomly assign one member of the pair to take the tutoring program and the other member not to take the program. You could also give a test of ability and match the pairs based on results of the test, matching the two with highest scores, the two with the next highest scores, and so on.
Questions 48 to 50: A researcher designed a study to assess whether grades in a statistics course could be improved by using a new teaching technique. The 250 students enrolled in a large introductory statistics class are also enrolled in one of 20 lab sections. The 20 lab sections are randomly divided into 2 groups of 10 lab sections each. The students in the first set of 10 lab sections are taught by this “new” method. The students in the remaining 10 lab sections are taught using the “old” techniques. The grades at the end of the term are then compared. Assume that the students do not know if the method they are being taught with is the old or the new method.
- What type of study is described above? Explain your answer.
KEY: An experiment since the researcher manipulated which lab received which teaching method and recorded the effect of this manipulation on the outcome of interest, namely, course grade.
- Identify the explanatory variable and the response variable in this study.
KEY: The explanatory variable is teaching method (with two levels of “old” versus “new”). The response variable is the course grade.
- Suppose the students in the “new” group were mostly upper-classmen and the students in the “old” group were mostly first and second-year students. What is the statistical name for the variable “year in school” in this study?
KEY: Year in school would be a confounding variable.
Section 6.3
- A case-control study found higher exposure to gases, dusts, and fumes in the workplace among patients with bronchitis (an inflammation of the lungs) than among patients without bronchitis. What type of study is this?
- Retrospective
- Prospective
KEY: A
- A sample of 16,000 women was randomly assigned to take HRT (Hormone Replacement Therapy) or a placebo for 8 years. The results found a larger proportion of heart attacks among women taking HRT than placebo. What type of study is this?
- Retrospective
- Prospective
KEY: B
- A difficult birth may put a baby at greater risk for autism, according to a study that may provide clues to the causes of the devastating neurological disability. The Centers for Disease Control and Prevention said that in a study of 698 Danish children who had the developmental disorder (autism), researchers found a disproportionately high number had been born before the 35^{th} week of pregnancy, had suffered from low birth weights and were in a breech position at birth. What type of study is this?
- Retrospective
- Prospective
KEY: A
- A tea manufacturer is trying to decide whether to add peach flavoring or mango flavoring to green tea for a new product. A study is done by stopping customers at a grocery store and asking them to drink a small cup of tea with each flavoring, then to rate each of the two flavors on a scale from 1 to 10. The order in which the teas are presented is randomly assigned for each person. What type of study is this?
- An observational study.
- A sample survey.
- A case-control study.
- A matched-pairs design.
KEY: D
- A researcher randomly sampled 100 students at a university and asked them if they regularly take vitamins. He also asked them how many colds they had in the last six months. He then compared the number of colds experienced by those who take vitamins to the number of colds experienced by those who don’t take vitamins. What type of study is this?
- Observational study
- Case control study
- Matched pairs study
- Randomized experiment
KEY: A
- In a study of acupuncture for treating pain 100 patients were recruited. Half were randomly assigned to receive acupuncture and the other half to receive a sham acupuncture treatment. The patients were followed for 6 months and the degree of pain relief measured. The patients did not know which treatment they actually received, but the treating physicians were aware of who was getting acupuncture and who wasn’t. Which of the following does not apply to this study?
- Randomized Experiment
- Retrospective Study
- Placebo Control
- Single Blind
KEY: B
- In a study of 62,641 female nurses the amount of selenium in toenail clippings was measured, and then they were followed for a number of years to determine the risk of cancer. Which of the following applies to this study?
- Randomized Experiment
- Prospective Study
- Placebo Control
- Single Blind
KEY: B
- A group of 709 patients with lung cancer was compared to a group of 709 controls. For each patient with lung cancer, a control patient from the same hospital and the same sex and age as the lung cancer patient was selected. The two groups were compared on their smoking habits. Which of the following applies to this study?
- Randomized Experiment
- Prospective Study
- Case–control Study
- Placebo Control
KEY: C
- A large international trial recruited 7,000 healthy women and randomly assigned them to receive either tamoxifen or a placebo. The women were followed for a number of years and the breast cancer rates were compared between the two groups. Neither the women nor the treating physicians knew which treatment the women were actually receiving. Which of the following does not apply to this study?
- Randomized Experiment
- Case–control study
- Placebo Control
- Double Blind
KEY: B
- In a Gallup telephone survey of 1001 adults done before the Thanksgiving holiday, 58% said they would like to lose a few pounds. Which of the following applies to this study?
- Randomized Experiment
- Observational Study
- Single Blind
- Double Blind
KEY: B
Questions 61 to 63: A difficult birth or a history of mental illness in a parent may put a baby at greater risk for autism. The Centers for Disease Control and Prevention said that in a study of 698 Danish children with the developmental disorder, researchers found a disproportionately high number had been born before the 35th week of pregnancy, had suffered from low birth weights and were in a breech position at birth. The children, all of whom were born after 1972 and diagnosed with autism before 2000, also were more likely to have a parent who had been diagnosed with schizophrenia-like psychosis before the autism was discovered.
- What type of study is this?
- A prospective observational study
- A retrospective observational study
- A case–control study
- An experiment
KEY: B
- What is the response variable in this study?
- time of birth (before or after week 35)
- birth weight (low or normal)
- birth position (breech or normal)
- presence of autism
KEY: D
- Which of the following applies to this study?
- Randomization
- Placebo Control
- Blinding
- None of the above
KEY: D
Questions 61 to 63: Very young children who live in homes where the television is on most of the time may have more trouble learning how to read than other kids their age, according to a study of media habits of children up to
6 years old. The report, based on a survey of parents, also found that kids in the 6 months to 6-year-old age group spend about two hours a day watching television, playing a video game or using a computer. That’s roughly the same amount of time they spend playing outdoors and three times as long as they spend reading or being read to.
- What type of study is this?
- A prospective observational study
- A retrospective observational study
- Case–control study
- An experiment
KEY: B
- What is the response variable in this study?
- Age of the child
- Ability to learn how to read
- Time spent playing outside
- Television habits in the home
KEY: B
- Which of the following applies to this study?
- Randomization
- Placebo Control
- Blinding
- None of the above
KEY: D
- You wish to study the effect of a tutoring program to help improve student grades in an introductory statistics course. Propose a retrospective study design to answer the question.
KEY: Ask students whether or not they took the tutoring program. Compare the grades of students who took the program with grades of those who didn’t. Confounding variables would be a problem in this study.
- You wish to study the effect of a tutoring program to help improve student grades in an introductory statistics course. Propose a prospective study design to answer the question.
KEY: Visit the tutoring program on the first day. Follow these students and the students not in the program as they take the statistics course. At the end of the course, compare the grades of students who took the program with grades of those who didn’t. Even better would be if you could randomly assign half of the students to participate in the tutoring program. This would turn the study into an experiment, instead of an observational study.
Section 6.4
- A distortion of results caused by the response of subjects to the special attention they receive from researchers is called
- extending results inappropriately.
- relying on memory or second hand sources.
- a cause and effect relationship.
- a Hawthorne
KEY: D
- When the results of a study on adults is applied to children, the effect is called
- extending results inappropriately.
- relying on memory or second hand sources.
- a cause and effect relationship.
- a Hawthorne
KEY: A
- When subjects receive subtle cues from the researchers about what outcomes are expected, the effect is called
- extending results inappropriately.
- relying on memory or second hand sources.
- a Hawthorne
- an Experimenter Effect.
KEY: D
- A survey of 1,204 black respondents found that 31% agreed with the statement “American society is fair to everyone” when the race of the interviewer was white, but only 14% agreed when the race of the interviewer was black. The difference between these responses is an example of
- extending results inappropriately.
- relying on memory or second hand sources.
- a Hawthorne Effect.
- an Experimenter Effect.
KEY: D
Questions 73 to 77: For each relationship, decide whether the variable is an interacting variable or a confounding variable.
- Nicotine patches have been shown to be effective in getting smokers to quit smoking. The therapy is even more effective when there are no other smokers in the home. The absence of other smokers in the home is
- a potential confounding variable.
- an interacting variable.
KEY: B
- The greater the hours of television watched, the lower the GPA (grade point average). The number of units (credit hours) taken is
- a potential confounding variable.
- an interacting variable.
KEY: A
- Suppose that a public television station found that the amount of donations following a promotional show was larger for women than for men. Gender is
- a potential confounding variable.
- an interacting variable.
KEY: B
- The effect of a pain relief medicine was much less if the user was under 50. Age is
- a potential confounding variable.
- an interacting variable.
KEY: B
- A professor found an association between the number of times a student came to office hours and the grade received in the course. The total number of hours that a student studied in the course is
- a potential confounding variable.
- an interacting variable.
KEY: A
Questions 78 to 80: Researchers would like to compare meditation and exercise to see which is more effective for reducing stress. One hundred people who suffer from high stress volunteer to participate in a study for ten weeks. Participants will either be given a 10-week course in meditation or will participate in a 10-week exercise program. The researchers must decide whether to randomly assign the volunteers to the two programs, or allow them to choose.
- Which of the following is the main advantage of randomly assigning participants to the two programs rather than allowing them to choose?
- The participants are more likely to stick with the program for the full 10 weeks.
- Confounding variables, such as past practice of meditation, should be approximately equal for the two groups.
- Random assignment ensures that the two sample sizes are equal and that requirement is necessary in studies like this one.
- Random assignment will allow the results to be extended to the population of all adults.
KEY: B
- Which of the following is an advantage of allowing participants to choose the program in which to participate?
- Allowing them to choose will increase the ecological validity of the study because in the real world people choose their own programs.
- Confounding variables, such as past practice of meditation, should be approximately equal for the two groups.
- Allowing participants to choose will allow the results to be extended to the population of all adults.
- If participants are allowed to choose then a cause and effect conclusion can be made.
KEY: A
- Suppose participants are randomly assigned to the two programs and a psychologist measures their stress levels before and after the 10-week program, without being told who is in which program. This experiment would be
- Single blind as long as the participants are not told the results of the stress level measurements.
- Single blind because the psychologist doesn’t know who is in which program, but the participants do know.
- Double blind as long as the participants are not told the results of the stress level measurements.
- Neither single nor double blind.
KEY: B
Questions 81 and 82: An observational study has found that drivers who report that they routinely wear a seatbelt were less likely to have been given a traffic ticket for speeding in the past three years.
- Of the following, which is the most likely explanation for this observed relationship?
- Police are less likely to stop a driver for speeding when they can see that he or she is wearing a seatbelt.
- People are less likely to speed when they are wearing a seatbelt.
- Confounding variables such as age and attention to risk factors in driving cause the same drivers who are likely to wear seatbelts to also be less likely to speed.
- Relying on memory has created a problem because most people don’t remember if they have had a speeding ticket in the past three years.
KEY: C
- A politician hears about this result and proposes a bill to finance a public education campaign to get people to wear seatbelts. He argues that if it works, it would reduce speeding as well. What would you conclude about his reasoning?
- It is correct.
- It is not correct because the relationship between seatbelt use and speeding tickets is probably due to confounding variables.
- It is not correct because the cause and effect relationship is most likely in the other direction.
- It is not correct because the results of an observational study cannot be extended to a population.
KEY: B
Questions 83 and 82: A study of changing speed limits in the United States finds no evidence that higher limits fuel more deaths. A scientist examined shifts in speed limit laws over the past few decades. Highway speed limits were initially throttled in the 1970s in response to the gas shortage. In the 1980s the focus shifted to public safety. Yet in 1995, Congress returned all speed limit authority back to the states, and many states raised their top highway speeds. While limits ranged from 75 mph to 55 and back again, no significant increase in fatalities per mile driven are evident. In fact, from 1968 to 1991, the fatality rate per 100 million miles declined by 63.2 percent. The scientist attributes the decrease to safer cars, increased use of seat belts, an increase in the minimum legal drinking age, and better road maintenance. “Automobile safety features and enforcement emerge as important factors in increasing highway safety,” the scientist contends. “Speed limits are far less important.”
- What type of study is described above?
- Prospective observational, because we already know that the speed limits were changed at the beginning of the study. We have to wait and see if the fatality rate has changed.
- Retrospective observational, because records were studied going all the way back to the 1970’s.
- An experiment, people have to actively drive their cars at these different speed limits.
KEY: B
- In the study “safer cars, increased use of seat belts, an increase in the minimum legal drinking age, and better road maintenance” are mentioned as reasons for a decline in the fatality rate between 1968 and 1991. What do we call these 4 variables?
- Response variables
- Qualitative variables
- Confounding variables
- Interacting variables
KEY: D
- If a statistically significant relationship is found in an observational study for which the sample represents the population of interest, then which of the following is true?
- A causal relationship cannot be concluded and the results cannot be extended to the population.
- A causal relationship can be concluded but the results cannot be extended to the population.
- A causal relationship cannot be concluded but the results can be extended to the population.
- A causal relationship can be concluded and the results can be extended to the population.
KEY: C
- What is the most likely problem for a randomized experiment that uses volunteers?
KEY: A common problem for experiments that use volunteers is extending results inappropriately. Common sense should enable you to figure out whether the volunteers in the study are representative of a larger population for that question.
- Explain which of the “difficulties and disasters” is most likely to be a problem in the following observational study and explain why. Successful female social workers and engineers were asked to recall whether they had any female professors in college who were particularly influential in their choice of career. More of the engineers than the social workers recalled a female professor who stood out in their minds.
KEY: Remembering the past would be a problem here. The women in social work were likely to have had a larger number of female professors, so no one would stand out in particular. The engineers may have had just one or two female professors, which would make those professors easier to remember.
Questions 88 to 90: A researcher wishes to see whether there is any difference in the average weight gains of athletes following one of three special diets (Diet 1, Diet 2, and Diet 3). The initial study design was to randomly assign the athletes to one of the three diet groups and place them on the diet for six weeks. The weight gain (in pounds) at the end of the six weeks would be recorded for each athlete.
- What type of study is this?
KEY: This is a randomized experiment.
- Gender was also recorded for this study. The results showed that the amount by which the weight gains for the three diets differed was affected by whether the athlete was a male or female. What is the statistical name for the variable gender in this case?
KEY: Gender is an explanatory variable that interacts with the principle explanatory variable (type of diet) in its relationship with the response variable (weight gain). The variable gender is an interacting variable.
- Suppose that 80% of the athletes are men and 20% of the athletes are women. In a randomized design it is possible that a diet (treatment) could have very few or no female athletes assigned to it. Suggest a way to improve on the design for the next study so as to control for the possible effects of gender.
KEY: A block design could be used with gender as the blocking variable. The female athletes would be randomly assigned to the three diets and then the male athletes would be randomly assigned to the three diets.
Mind on Statistics Test Bank
Chapter 7
Sections 7.1 – 7.2
Questions 1 to 6: For each situation, decide if the probability described is a subjective (personal) probability or a relative frequency probability.
- In a sample of 1000 students majoring in the humanities, 660 were female. The 66% (660/1000) chance of a humanities major being female is a
- subjective probability.
- relative frequency probability.
KEY: B
- A quarter is flipped 2000 times and results in 500 heads. The 25% (500/2000) chance of heads is a
- subjective probability.
- relative frequency probability.
KEY: B
- Among 5000 new tires sold by a tire company, 20% (1000/5000) lasted more than 100,000 miles. The 20% chance that a new tire will last more than 100,000 miles is a
- subjective probability.
- relative frequency probability.
KEY: B
- A football fan believes that the Oakland Raiders have a 50% chance of winning the next Super bowl. The 50% is a
- subjective probability
- relative frequency probability
KEY: A
- A college basketball player has made 53% of his shots from 3-point range. The probability that he will make a 3-point shot, 53%, is a
- subjective probability.
- relative frequency probability.
KEY: B
- A recent college graduate claims he only has a 30% chance of finding a job in the next two months. The chance of 30% is a
- subjective probability.
- relative frequency probability.
KEY: A
Questions 7 and 8: In the past five years, only 5% of pre-school children did not improve their swimming skills after taking a Beginner Swimmer Class at a certain Recreation Center.
- The probability of 5% that a pre-school child who is taking this swim class will not improve his/her swimming skills is a
- subjective probability.
- relative frequency probability.
KEY: B
- What is the probability that a pre-school child who is taking this swim class will improve his/her swimming skills?
- 5%
- 10%
- 95%
- None of the above
KEY: C
- A survey was given to sophomores at a university and one of the questions asked was “What is the probability that you will leave school before you graduate?” The answer to this question for an individual student is an example of
- a relative frequency probability based on long-run observation.
- a relative frequency probability based on physical assumptions.
- a personal probability.
- a probability based on measuring a representative sample and observing relative frequencies that fall into various categories.
KEY: C
- A thumbtack is tossed repeatedly and observed to see if the point lands resting on the floor or sticking up in the air. The goal is to estimate the probability that a thumbtack would land with the point up. That probability is an example of
- a relative frequency probability based on long-run observation.
- a relative frequency probability based on physical assumptions.
- a personal probability.
- a probability based on measuring a representative sample and observing relative frequencies that fall into various categories.
KEY: A
- Which of the following is an example of a relative frequency probability based on measuring a representative sample and observing relative frequencies of possible outcomes?
- According to the late Carl Sagan, the probability that the earth will be hit by a civilization-threatening asteroid in the next century is about 0.001.
- If you flip a fair coin, the probability that it lands with heads up is ½.
- Based on a recent Newsweek poll, the probability that a randomly selected adult in the US would say they oppose federal funding for stem cell research is about 0.37.
- A new airline boasts that the probability that its flights will be on time is 0.92, because 92% of all flights it has ever flown did arrive on time.
KEY: C
- A survey was given to sophomores at a university and one of the questions asked was “What is the probability that you will leave school before you graduate?” The answer to this question for an individual student is an example of
- a relative frequency probability based on long-run observation.
- a relative frequency probability based on physical assumptions.
- a probability based on measuring a representative sample and observing relative frequencies that fall into various categories.
- a personal probability.
KEY: D
- Students at a university who apply for campus housing can be assigned to live in a dormitory room, a suite in a dormitory or an apartment. If Alice has a 0.30 chance of being assigned to a dormitory room and a 0.50 chance of being assigned to a suite in a dormitory, what is the probability that she will be assigned to an apartment?
KEY: 0.20
- When a fair coin is tossed two times, there is a 25% chance of getting 0 heads and a 50% chance of getting 1 head. What is the chance of getting 2 heads?
KEY: 25%
- When 2 cards are drawn at random from a standard 52-card deck, there is a 0.8507 chance of drawing 0 Aces, and a 0.1448 chance of drawing 1 Ace. What is the chance of drawing 2 Aces?
KEY: 0.0045
- A plane flies over the ocean in search of schools of fish. On any given day, there is a 0.07 chance of finding 2 or more schools of fish, and a 0.28 chance of finding only one school of fish. What is the chance the day of searching results in not finding any schools of fish at all?
KEY: 0.65
- When two dice are rolled, there are 36 possible outcomes. Six of these outcomes have two the same numbers (two ones, two twos, etc.). The chance of getting two of the same numbers when rolling two dice is 6/36 or 0.1667. What is the chance of getting 2 numbers that are different from one another?
KEY: 0.8333
- Every year, on the first day of school, the sixth grade teacher at Greenville Middle School asks his students to pick their favorite primary color: red, yellow, or blue. From years of experience, the teacher knows that only 1 in 7 students choose yellow and that about half of the students pick blue. What is the chance that a student picks red?
KEY: 0.357
- The lifetime risk for a woman to develop breast cancer is estimated to be about 1 in 8. Express this probability as a fraction, as a proportion, and as a percentage.
KEY: fraction = 1/8; proportion = 0.125; percentage = 12.5%
Section 7.3
Questions 20 to 23: A statistics class has 4 teaching assistants (TAs): three female assistants (Lauren, Rona, and Leila) and one male assistant (Josh). Each TA teaches one discussion section.
- A student picks a discussion section. The two events W = {the TA is a woman} and J = {the TA is Josh} are
- independent events.
- disjoint (mutually exclusive) events.
- each simple events.
- None of the above.
KEY: B
- A student picks a discussion section. The events L = {the TA is Lauren} and R = {the TA is Rona} are
- independent events.
- disjoint (mutually exclusive) events.
- each simple events.
- None of the above.
KEY: Both B and C
- A student picks a discussion section. The two events W = {the TA is a woman} and M = {the TA is a man} are
- independent events.
- disjoint (mutually exclusive) events.
- each simple events.
- None of the above.
KEY: B
- Two students, Bill and Tom, who don’t know each other, each pick a discussion section. The two events
B = {Bill’s TA is Lauren} and T = {Tom’s TA is a woman} are- independent events.
- disjoint (mutually exclusive) events.
- each simple events.
- None of the above.
KEY: A
Questions 24 to 27: Students who live in the dorms at a college get free T.V. service in their rooms, but only receive 6 stations. On a certain evening, a student wants to watch T.V. and the six stations are broadcasting separate shows on baseball, football, basketball, local news, national news, and international news. The student is too tired to check which channels the shows are playing on, so the student picks a channel at random.
- The two events A = {the student watches an athletic event} and N = {the student watches a news broadcast} are
- independent events.
- disjoint (mutually exclusive) events.
- each simple events.
- None of the above.
KEY: B
- The events F = {the student watches football} and B = {the student watches baseball} are
- independent events.
- disjoint (mutually exclusive) events.
- each simple events.
- None of the above.
KEY: Both B and C
- The two events F = {the student watches football} and A = {the student watches an athletic event} are
- independent events.
- disjoint (mutually exclusive) events.
- each simple events.
- None of the above.
KEY: D
- On a different night, two students who don’t know each other each choose a channel this way. The two events, N = {the first student watches a news broadcast } and F = {the second student watches football} are
- independent events.
- disjoint (mutually exclusive) events.
- each simple events.
- None of the above.
KEY: A
- Lauren wants to wear something warm when she leaves for class. She reaches into her coat closet without looking and grabs a hanger. Based on what she has in her coat closet, she has a 30% chance of picking a sweater, a 50% chance of picking a coat, and a 20% chance of picking a jacket. What is the probability that she will pick a sweater or a coat?
- 15%
- 30%
- 50%
- 80%
KEY: D
- A birth is selected at random. Define events B = {the baby is a boy} and F = {the mother had the flu during her pregnancy}. The events B and F are
- disjoint but not independent.
- independent but not disjoint.
- disjoint and independent.
- neither disjoint nor independent.
KEY: B
Questions 30 and 31: A student is randomly selected from a large college campus. Define the events
H = {the student has blond hair} and E = {the student has blue eyes}.
- The events H and E are
- disjoint but not independent.
- independent but not disjoint.
- disjoint and independent.
- neither disjoint nor independent.
KEY: D
- The chance that a blond haired student has blue eyes equals 75%. How do we write this probability?
- P(H) = 0.75
- P(E) = 0.75
- P(E|H) = 0.75
- P(H|E) = 0.75
KEY: C
Questions 32 to 34: A student is randomly selected from a large college. Define the events C = {the student owns a cell phone} and I = {the student owns an iPod}.
- Which of the following is the correct interpretation of the probability P(I|C)?
- The chance that a randomly selected student owns an iPod.
- The percentage of students who own both a cell phone and an iPod.
- The proportion of students who own a cell phone who also own an iPod.
- The relative frequency of iPod owners who own a cell phone.
KEY: C
- Which of the following is the correct notation for the percentage of students who own a cell phone but not an iPod?
- P(C|I)
- P(C|I^{C})
- P(C^{C} and I)
- P(C and I^{C})
KEY: D
- Suppose you know that your friend’s sister, who attends this college, owns a cell phone and you are wondering what would be the chance that she owns an iPod. What type of probability would this be?
- A probability of independent events.
- A probability of dependent events.
- A conditional probability.
- A probability of disjoint events.
KEY: C
Questions 35 to 37: A football player is randomly selected from all NCAA Division I college teams. Define the events D = {the football player plays defense} and T = {the football player is over 6 feet tall}.
- How do we interpret the probability P(D|T)?
KEY: The proportion (or percentage) of tall football players (players over 6 feet) who play defense.
- Suppose the percentage of football players who play defense that are shorter than 6 feet tall is only 8%. How do write this statement using events D and T?
KEY: P(T^{C}|D) = 0.08
- Refer to question 36. Suppose that we also know that of all NCAA Division I football players, 15% are shorter than 6 feet. What do we know about events D and T?
- They are independent events.
- They are dependent events.
- They are disjoint events.
KEY: B
- At a particular university, a study has shown that students who live on campus are more likely to have GPAs over 3.0 than students who do not. A freshman at this university is randomly selected at the beginning of the fall term. Define events A = {the student lives on campus}, and B = {the student has a GPA over 3.0 at the end of the fall term}. According to the housing office, P(A) = .80. Which statement is definitely true about P(B|A) based on this information?
- P(B|A) = .80
- P(B|A) is greater than P(B|not A)
- P(B|A) is less than P(B|not A)
- P(B|A) = P(B|not A)
KEY: B
Section 7.4
- Michael wants to take French or Spanish, or both. But classes are closed, and he must apply and get accepted to be allowed to enroll in a language class. He has a 50% chance of being admitted to French, a 50% chance of being admitted to Spanish, and a 20% chance of being admitted to both French and Spanish. If he applies to both French and Spanish, the probability that he will be enrolled in either French or Spanish (or possibly both) is
- 70%
- 80%
- 90%
- 100%
KEY: B
- If one card is randomly picked from a standard deck of 52 cards, the probability that the card will be a number from 2 through 10, or a Heart, or both, is
- 9% (27/52)
- 2% (36/52)
- 9% (40/52)
- 2% (49.52)
KEY: C
- If one card is randomly picked from a standard deck of 52 cards, the probability that the card will be a red suit (Heart or Diamond), or a face card (Jack, Queen, or King), or both, is
- 0% (26/52)
- 5% (32/52)
- 9% (40/52)
- 5% (46/52)
KEY: B
Questions 42 to 44: A standard 52-card deck is shuffled and 2 cards are picked from the top of the deck.
- The probability that the first card is a Heart and the second card is a Spade is
- 9%
- 3%
- 4%
- 0%
KEY: C
- The probability that the both cards are Hearts is
- 3%
- 9%
- 4%
- 0%
KEY: B
- The probability that the first card is a face card (Jack, Queen, King) and the second card is not a face card is
- 3%
- 8%
- 1%
- 2%
KEY: C
- Two standard 52-card decks are shuffled and two cards are picked at random — one card from each deck. The probability that two Hearts are drawn is
- 9%
- 3%
- 0 %
- 0%
KEY: B
Questions 46 and 47: A card is drawn at random from a standard 52-card deck.
- The conditional probability that the card is a King given that a face card (Jack, Queen, or King) was drawn is
- 0% (1/5)
- 0% (1/4)
- 3% (1/3)
- 0% (1/2)
KEY: C
- The conditional probability that the card is a 2 given that a 2 or a 3 was drawn is
- 0% (1/5)
- 0% (1/4)
- 3% (1/3)
- 0% (1/2)
KEY: D
- A soft drink company holds a contest in which a prize may be revealed on the inside of the bottle cap. The probability that each bottle cap reveals a prize is 0.2 and winning is independent from one bottle to the next. What is the probability that a customer must open three or more bottles before winning a prize?
- (0.2)(0.2)(0.8) = 0.032
- (0.8)(0.8)(0.2) = 0.128
- (0.8)(0.8) = 0.64
- 1 – (0.2)(0.2)(0.8) = .968
KEY: C
Questions 49 and 50: Suppose two different states each pick a two-digit lottery number between 00 and 99 (for a 100 possible numbers).
- What is the probability that both states pick the number 13?
- 2/100
- 1/100
- 1/200
- 1/10,000
KEY: D
- What is the probability that both states pick the same number?
- 2/100
- 1/100
- 1/200
- 1/10,000
KEY: B
- A six-sided die is made that has four Green sides and two Red sides, all equally likely to land face up when the die is tossed. The die is tossed three times. Which of these sequences (in the order shown) has the highest probability?
- Green, Green, Green
- Green, Green, Red
- Green, Red, Red
- They are all equally likely
KEY: A
Questions 52 to 55: A student doing an internship at a large research firm collected the following data, representing all of the studies the firm had conducted over the past 3 years.
Type of study | |||
Randomization part of study? | Retro. Observational | Pro. Observational | Experiment |
Yes | 7 | 28 | 35 |
No | 53 | 62 | 115 |
- Suppose one study is to be randomly selected from all studies conducted over the past 3 years by this large research firm. What is the probability that this study used randomization?
- 1167
- 2333
- 26
- 3111
KEY: B
- What is the probability that the study used randomization, if we already know that the study was a retrospective observational study?
- 1167
- 2333
- 26
- 3111
KEY: A
- Define the events E = {the study was an experiment}, U = {the study used randomization} and R = {the study was a retrospective observational study}. Which of the following sets of events are disjoint?
- E and U
- E and R
- U and R
- All three
- None of the above
KEY: B
- Define the events E = {the study was an experiment} and U = {the study used randomization}. Are the events E and U independent?
- Yes
- No
- Can’t tell
- Need more information to determine this.
KEY: A
Questions 56 to 60: For each of the following statements, determine if they are true or false.
- If two events A and B are independent, they must also be mutually exclusive.
- True
- False
KEY: B
- If two events A and B are mutually exclusive, they must also be independent.
- True
- False
KEY: B
- The probability of the intersection of two events A and B, and the probability of the union of A and B can never be equal.
- True
- False
KEY: B
- If events A and B are known to be independent and P(A) = 0.2 and P(B) = 0.3, then P(A and B) = 0.5.
- True
- False
KEY: B
- If events D and E are known to be mutually exclusive, then P(D|E) = 0.
- True
- False
KEY: A
- Which of the following is definitely true for mutually exclusive events A and B?
- P(A) = 1 – P(B)
- P(A) + P(B) = 1
- P(A and B) = P(A)P(B)
- P(A and B) = 0
KEY: D
- Suppose that the probability of event A is 0.2 and the probability of event B is 0.4. Also, suppose that the two events are independent. Then P(A|B) is:
- P(A) = 0.2
- P(A) / P(B) = 0.2/0.4 = ½
- P(A)P(B) = (0.2)(0.4) = 0.08
- None of the above.
KEY: A
- When two cards are drawn at random from a 52 card deck, the probability of drawing one Jack is 0.145. The probability of drawing one Ace is 0.145, and the probability of drawing a Jack and an Ace is 0.012. What is the probability of drawing a Jack or an Ace?
KEY: 0.278
Questions 64 and 65: When a fair coin is flipped 6 times, the probability of getting an odd number of heads
(1, 3, or 5) is 0.5.
- What is the probability of getting an even number of heads (0, 2, 4, or 6)?
KEY: 0.5
- The probability of getting more than 3 heads is 0.344, and the probability of getting 5 heads is 0.094. What is the probability of getting either an odd number of heads or more than 3 heads?
KEY: 0.75
Questions 66 to 68: A mail-order company classifies its customers by gender (male/female) and by location of residence (urban/suburban). The market research department has determined that 2/3 of their customers are female and that 75% of their customers live in the suburbs. They have also determined that gender and location of residence seem to be independent of one another.
- If the mail order company will randomly select one of their customers, what is the probability that it will be a suburban female?
KEY: 50%
- The mail order company will randomly select one of their customers. Suppose we know they have selected a person in the suburbs. What is the probability that this person is female?
KEY: 2/3
- Making up the majority of their customers, the females and suburban customers are identified as the focus group for their new ad campaign. If the mail order company will randomly select one of their customers, what is the probability that it will be a suburban customer or a female?
KEY: 0.9167
Questions 69 to 72: A study was conducted at a small college on first-year students living on campus. A number of variables were measured. The table below provides information regarding number of roommates and end of term health status for the first-year students at this college. Health status for individuals is measured as poor, average, and exceptional.
Number of roommates | |||
Health status | None | One | Two |
poor | 15 | 36 | 65 |
average | 35 | 94 | 40 |
exceptional | 50 | 50 | 25 |
- What is the probability that a randomly selected first-year student with no roommates had poor end of term health status?
KEY: 0.15
- What is the probability that a randomly selected first-year student with 1 roommate had poor end of term health status?
KEY: 0.20
- Are the events H = {the student has poor health status} and N = {the student has no roommates} mutually exclusive?
KEY: No
- Are the events H = {the student has poor health status} and N = {the student has no roommates} independent?
KEY: No
Questions 73 to 76: The following table provides information regarding health status and smoking status of residents of a small community (health status for individuals was measured by the number of visits to the hospital during the year).
Smoker Status | ||
Visits | Smoker | Nonsmoker |
None | 20 | 100 |
Few | 70 | 90 |
Many | 90 | 30 |
- What is the probability that a randomly selected resident made zero visits to the hospital?
KEY: 0.30
- What is the probability that a randomly selected nonsmoker made zero visits to the hospital?
KEY: 0.4545
- Are the events N = {the resident does not smoke} and Z = {the resident made zero visits to the hospital} mutually exclusive?
KEY: No
- Are the events N = {the resident does not smoke} and Z = {the resident made zero visits to the hospital} independent?
KEY: No
Questions 77 to 80: In a survey of 1000 adults, respondents were asked about the expense of a college education and the relative necessity of financial assistance. The correspondents were classified as to whether they currently had a child in college or not (college status), and whether they thought the loan obligation for most college students was too high, about right, or too little (loan obligation opinion). The table below summarizes some of the survey results. Use these results to answer the following questions.
Loan Obligation Opinion | ||||
College Status | Too High | About Right | Too Little | Total |
Child in College | 350 | 80 | 10 | 440 |
No Child in College | 250 | 200 | 110 | 560 |
- What is the probability that a randomly selected adult will think loan obligations are too high?
KEY: P(Too High) = 600/1000 = .60
- What is the probability that a randomly selected adult with a child in college will think loan obligations are too high?
KEY: P(Too High | Child in College) = 350/440 = .795
- Are the events H = {the adult thinks loan obligations are too high} and C = {the adult has a child in college} mutually exclusive?
KEY: No, there are 350 adults that make up the event “H and C”, so the intersection is not empty.
- Are the events H = {the adult thinks loan obligations are too high} and C = {the adult has a child in college} independent?
KEY: No, the probability of thinking loan obligations are too high does change if we know the adult has a child in college; namely P(H | C) = .795 does not equal P(H) = .60.
Sections 7.5 – 7.6
Questions 81 and 82: A standard 52-card deck is shuffled and 5 cards are picked from the top of the deck.
- The probability that the first four cards are a red suit (Heart or Diamond) and the last card is a black suit (Spade or Club) is
- 53%
- 99%
- 13%
- 0%
KEY: B
- The probability that the first four cards are Aces and the last card is a 2 is
- 1 ´ 10^{-7}
- 7 ´ 10^{-6}
- 7 ´ 10^{-6}
- 077
KEY: A
- A short quiz has two true-false questions and one multiple-choice question with four choices. A student guesses at each question. Assuming the choices are all equally likely, what is the probability that the student gets all three correct?
- 1/32
- 1/3
- 1/8
- 1/16
KEY: D
- Four students’ names, including yours, are written on separate slips of paper and placed in a box. The teacher randomly draws two names without replacement. What is the probability that the paper with your name on it will be the second one drawn?
- 1/4
- 1/3
- 1/2
- 3/4
KEY: A
- A medical treatment has a success rate of 0.8. Two patients will be treated with this treatment. Assuming the results are independent for the two patients, what is the probability that neither one of them will be successfully cured?
- 5
- 36
- 2
- 04
KEY: D
- Elizabeth has just put 4 new spark plugs in her car. For each spark plug, the probability that it will fail in the next 50,000 miles is 1/100 (which is 0.01), and is independent from one spark plug to the next. What is the probability that none of the spark plugs will fail in the next 50,000 miles?
- (0.01)(0.01)(0.01)(0.01)
- 1 – (0.01)(0.01)(0.01)(0.01)
- (0.99)(0.99)(0.99)(0.99)
- 1 – (0.99)(0.99)(0.99)(0.99)
KEY: C
- Tree diagrams are most useful for finding probabilities when
- all of the events involved are independent.
- all of the events involved are mutually exclusive.
- each random circumstance has three or more possible outcomes.
- conditional probabilities are known in one direction, say P(A|B) and you are trying to find them for the other direction, say P(B|A).
KEY: D
- Tickets for an upcoming concert are sold out but a local charity is having a raffle and the prize is a pair of tickets to the concert. One hundred people enter the raffle, so each individual who entered has 1/100 probability of winning the pair of tickets. You and a friend both entered. What is the probability that one or the other of you wins the tickets?
- 1/100
- 2/100
- (1/100)(1/100)
- 2/100 – (1/100)(1/100)
KEY: B
Questions 89 to 91: Thirty percent of the students in a high school face a disciplinary action of some kind before they graduate. Of those students, 40% go on to college. Of the 70% who do not face a disciplinary action, 60% go on to college.
- What percent of the students from the high school go on to college?
- 12%
- 42%
- 50%
- 54%
KEY: D
- What is the probability that a randomly selected student both faced a disciplinary action and went on to college?
- 12
- 40
- 42
- 84
KEY: A
- Given that a randomly selected student goes on to college, what is the probability that he or she faced a disciplinary action?
- 12
- 22
- 30
- 78
KEY: B
- Which of the following is not necessarily true for independent events A and B?
- P(A and B) = P(A)P(B)
- P(A|B)=P(A)
- P(B|A)=P(B)
- P(A or B) = P(A) + P(B)
KEY: D
- If events A and B are mutually exclusive (disjoint) then
- they must also be independent.
- they cannot also be independent.
- they must also be complements.
- they cannot also be complements.
KEY: B
- A new drug is successful 80% of the time. A student would like to simulate the probability that if 5 people are given the drug it will be successful on exactly 3 of them. She will randomly choose digits with equal probability from 0, 1, 2, …, 9 to represent each individual. How should she assign outcomes?
- Digits 0 to 2 represent successful treatment while digits 3 to 9 represent failure.
- Digits 0 to 4 represent successful treatment while digits 4 to 9 represent failure.
- Digits 0 to 7 represent successful treatment while digits 8 and 9 represent failure.
- Digits 0 to 8 represent successful treatment while digit 9 represents failure.
KEY: C
Questions 95 to 97: In the Banana Republic there are two producers of PCs, referred to as Pac and Bell. Assume that there are no PC imports. The market shares for these two producers are 70% for Pac and 30% for Bell. One executive at Bell proposes a longer warranty period (similar to one given by auto makers) to be offered at a slight extra cost as a plan to increase market share. A market research company appointed by Bell conducts a census of PC owners on their opinion of this warranty proposal. Among owners of a PC made by Pac, 50% like the proposal, 30% are indifferent to it, while the remaining owners oppose it. Among owners of a PC made by Bell, 70% like the proposal, 20% are indifferent to it, and the remaining owners oppose it.
- A PC owner will be selected at random. What is the probability that the person will own a PC made by Bell?
KEY: 0.30
- A PC owner will be selected at random. What is the probability that the owner will be opposed to the proposal of a new warranty at extra cost?
KEY: 0.17
- Suppose the selected PC owner is opposed to the new proposal. What is the conditional probability that the person is an owner of a PC made by Bell?
KEY: 0.1765
Questions 98 to 100: Of the residents of the U.S., 43% live in Northeast/Midwest region while the remaining 57% live in the South/West region. Of the residents in the Northeast/Midwest region, 14% are senior citizens, while the corresponding value for the South/West region is 12%. A citizen will be selected at random.
- What is the probability that the person will be a senior citizen?
KEY: 0.1286
- What is the probability that the person will be a senior citizen from the Northeast/Midwest region?
KEY: 0.0602
- What is the probability that the person will be from the Northeast/Midwest region, given that he/she is a senior citizen?
KEY: 0.4681
- The statistics of a particular basketball player state that he makes, on average, 4 out of every 5 free throw attempts. This player is about to make 5 free throw attempts. We wish to calculate the probability that all 5 attempts result in a goal. Explain how you would choose random digits to simulate this scenario.
KEY: Generate random numbers between 1 and 5. Digits 1 to 4 will represent a goal and the 5 will represent a miss. Each repetition will consist of 5 values. Anytime we see a sequence without a 5, all attempts result in a goal.
- A standard deck of cards has 52 cards. The cards have one of 4 suites: 13 cards are hearts, 13 cards are diamonds, 13 cards are clubs, and 13 cards are spades. We will draw cards from a shuffled deck of cards with replacement (after we draw each card, we will record the suite and put it back in the deck). We will keep going until we draw hearts. We wish to calculate the probability of having to draw 3 or fewer cards. Explain how you would choose random digits to simulate this scenario.
KEY: Generate random numbers between 1 and 4. The 1 will represent hearts; the 2, 3, and 4 will represent the other suits. Every time we simulate this process, keep going until observing a 1.
- Belgium has two official languages, French and Dutch. Assume that about 60% of the people use Dutch as their primary language and 40% of the people use French as their primary language. We are about to randomly select 3 Belgians. We wish to calculate the probability that the 3 people speak the same language. Explain how you would choose random digits to simulate this scenario.
KEY: Generate random numbers between 1 and 5. The 1, 2 and 3 will represent Dutch, the 4 and 5 will represent French. Each repetition will consist of 3 values. Any time we see all 1, 2, and 3’s or only 4 and 5’s, all people speak the same language.
- When 4 cards are drawn randomly from a standard 52-card deck without replacement, what is the probability that the first two cards are Hearts and the second two cards are Spades?
KEY: 0.00375
Section 7.7
- A test to detect prostate cancer in men has a sensitivity of 95%. This means that
- 95% of the men who test positive will actually have prostate cancer.
- 95% of the men with prostate cancer will test positive.
- 95% of the men who do not have prostate cancer will test negative.
- 95% of the men who test negative will actually not have prostate cancer.
KEY: B
- A test to detect prostate cancer in men has a specificity of 80%. This means that
- 80% of the men who test positive will actually have prostate cancer.
- 80% of the men with prostate cancer will test positive.
- 80% of the men who do not have prostate cancer will test negative.
- 80% of the men who test negative will actually not have prostate cancer.
KEY: C
- Which of the following statements is true for 6 tosses of a fair coin, where H = Heads and T = Tails?
- Sequences with all heads, like HHHHHH, are less likely than specific sequences with 3 heads and 3 tails, like HTHTHT.
- Sequences with all heads, like HHHHHH, are more likely than specific sequences with 3 heads and 3 tails, like HTHTHT.
- All specific sequences six letters long (made up of H’s and T’s), regardless of the number of H’s and T’s, are equally likely.
- None of the above.
KEY: C
- Which of the following statements is true for tossing a fair coin (i.e. Probability of Heads = ½) if the first 100 tosses of the coin result in 100 heads?
- The chance that the next toss will be heads is almost certain.
- The chance that the next toss will be heads is nearly 0.
- The chance that the next toss will be heads is ½.
- None of the above.
KEY: C
- Imagine a test for a certain disease. Suppose the probability of a positive test result is 0.95 if someone has the disease, but the probability is only 0.08 that someone has the disease if his or her test result was positive. A patient receives a positive test, and the doctor tells him that he is very likely to have the disease. The doctor’s response is
- an example of “Confusion of the inverse.”
- an example of the “Law of small numbers.”
- an example of “The gambler’s fallacy.”
- correct, because the test is 95% accurate when someone has the disease.
KEY: A
- Consider the following three sequences of outcomes after tossing 6 coins: HHHHHH, HHHTTT, and HTHHTH. Which of the following represents the ordering of these three sequences in order of highest to lowest probability?
- HTHHTH, HHHTTT, HHHHHH
- HTHHTH, HHHTTT, HHHHHH
- All three equally likely.
- None of the above.
KEY: C
- Consider the following three descriptions of outcomes after tossing 6 coins: {all six heads}, {3 heads and 3 tails (in any order)}, and {4 heads and 2 tails (in any order)}. Which of the following represents the ordering of these three descriptions in order of highest to lowest probability?
- {3 heads and 3 tails}, {all six heads}, {4 heads and 2 tails}
- {3 heads and 3 tails}, {4 heads and 2 tails}, {all six heads}
- All three equally likely.
- None of the above.
KEY: B
Questions 112 and 113: It seems that every year we hear about a train derailment. Discussions about the safety of train travel are initiated each time. Suppose there have been nine fatal train derailments over the past 10 years. However, each year, 5 million train trips depart (this does not include subway travel).
- What is the relative frequency of fatal train derailments?
KEY: Roughly 1 per year or roughly 1 per every 5 million train trips.
- Which of the following is not a correct interpretation of these numbers?
- In the long run about 1 out of every 5 million train trips will end in a fatal derailment.
- The probability that you will be in a fatal train derailment is 1 in 5 million.
- The probability that a randomly selected train trip will end in a fatal derailment is about 1/5,000,000.
- None of the above, all statements are correct.
KEY: B
- Assuming that a person has an equal chance of being born on any day of a 365-day year, what is the chance that two people chosen at random will have different birthdays?
KEY: 99.7%