Deck 1: Collecting Data in Reasonable Ways

Question 1

By definition, a simple random sample of size n is any sample that is selected in a manner to guarantee every individual in the population has an equal chance of selection.

Answer 1

False

Question 2

A placebo is identical in appearance to the treatment of interest, but contains no active ingredients.

Answer 2

True

Question 3

A control group provides a baseline for comparison to a treatment group.

Answer 3

True

Question 4

Clusters are non-overlapping subgroups of a population that have been identified as homogeneous.

Question 5

A treatment is any particular combination of values for the explanatory variables.

Question 6

The method of control wherein an extraneous variable is held constant is called blocking.

Question 7

Two factors are extraneous if their effects on the response variable cannot be distinguished from one another.

Question 8

Increasing sample size will generally eliminate bias in a sample.

Question 9

Response bias can occur when responses are not actually obtained from all individuals selected for inclusion in the sample.

Question 10

Random assignment of volunteers should result in comparable experimental groups.

Question 11

A study is an observational study if the investigator observes the behavior of a response variable when one or more factors are manipulated.

Question 12

Stratified sampling is a sampling method that in no way involves simple random sampling.

Question 13

The entire collection of individuals or objects about which information is desired is called a sample.

Question 14

Random subpopulations of a population are called strata.

Question 15

Selection bias can occur if volunteers only are used in a study.

Question 16

Random assignment to treatments will guarantee groups that are exactly alike for experimental purposes.

Question 17

Blocking is a technique that can be used to filter out the effects of extraneous factors.

Question 18

If the subjects as well as the person measuring the response are aware of the treatment assigned to the subject, only single-blinding is being used.

Question 19

In a well-designed experiment, the factors are confounded whenever possible.

Question 20

As long as the sample size is small relative to the population, there is little practical difference between sampling with replacement and sampling without replacement.

Question 21

Select the correct sampling method for the following situation. ​
To analyze the level of employee satisfaction at stores in a certain large city, a grocery store chain selects eight store locations at random and surveys all employees at these locations.
​

A)Simple random sampling
B)Stratified random sampling
C)Cluster sampling
D)Systematic sampling
E)Convenience sampling

Question 22

We have distinguished two types of studies: observational and experimental. Briefly explain the essential difference(s) between these two types of study.

Question 23

Briefly describe how populations and samples differ.

Question 24

Which of the following statistical studies is an experimental study? ​

A)A researcher observes the effect of alcohol consumption on reaction time by administering various quantities of alcohol to randomly-selected subjects.
B)A study is conducted to see if exposure to increased carbon dioxide levels increases tomato yields.Tomato plants are selected at random and are then exposed to various doses of carbon dioxide.
C)Two random samples of senior adults are selected.The first group watches a 30-minute presentation on medicare fraud, while the other group does not watch the presentation.A survey is then administered to measure the level of confidence the subjects have in their health care providers.
D)All of these are experimental studies.
E)None of these are experimental studies.

Question 25

The most basic sampling method studied in statistics is the simple random sample (SRS). In your own words, what is the correct definition of a simple random sample of size n?

Question 26

The ZZZ chain of motels has a standard method of constructing their rooms to maximize the ease of parking for its customers. The rooms are arranged in adjacent buildings so that each customer can park outside the rented room. The layout for one of the hotels with 48 rooms located along a famous highway is diagrammed below: Route 66
​ ​ The manager would like to survey customers in 12 of his rooms (one randomly selected customer for each room selected in the sample) to assess their satisfaction with the motel services. The surveys will be placed on the customers' beds before they check in to the motel. In order to make the directions easy to follow, he elects to use systematic sampling.
(a)Explain how you would use random numbers to set up the systematic sampling process.
(b)Write a short paragraph for the maids that helps them carry out your method in part (a).

Question 27

For which of the following types of studies is it impossible to draw cause-and effect conclusions? I). Completely randomized experiments
II)) Randomized block experiments
III). Observational studies

A)I only
B)II only
C)III only
D)It is never possible to draw cause-and-effect conclusions.
E)It is always possible to draw cause-and-effect conclusions.

Question 28

To estimate the proportion of students who plan to purchase tickets to an upcoming school fundraiser, a high school decides to sample 100 students as they register for the spring semester. There are 2000 students at the school. Which of the following sampling plans would result in a simple random sample? ​

A)Number the students from 1 to 2000 and then use random numbers to select 100 students.
B)Survey the first 100 students to register.
C)Randomly select 100 students from a list of the 950 female students at the school.
D)Divide the students into early registrants (the first 1000 to register) and late registrants (the last 1000 to register).Use random numbers to identify 50 of the early registrants and 50 of the late registrants to survey.
E)Select one of the first 20 students to register using a random number table and then select every 20th student to register thereafter.

Question 29

Bias, the tendency for samples to differ from the corresponding population in some systematic way, might be due to: (a) selection bias, (b) response bias, and/or (c) nonresponse bias. In a few sentences, discuss the differences among these different biases.

Question 30

The following paragraph describes an actual study. After reading the description, determine whether the study is an observational or experimental study. Justify your answer with specific references to the information in the study.
​
"Before the opening of the new International Airport and the termination of the old airport, children near both sites were recruited into aircraft-noise groups (aircraft noise at present or pending) and control groups with no aircraft noise and closely matched for socio-economic status. A total of 326 children (mean age = 10.4 years) took part in three data-collection waves, one before and two after the switch-over of the airports. After the switch to the new airport, long-term memory and reading were found to be impaired in the noise group at the new airport, and improved in the formerly noise-exposed group at the old airport."

Question 31

Which of the following best summarizes "nonresponse bias"? ​

A)a tendency for samples to differ from the corresponding population as a result of systematic exclusion of some part of the population
B)a tendency for samples to differ from the corresponding population because data are not obtained from all individuals selected for inclusion in the sample
C)a tendency for samples to differ from the corresponding population because the method of observation tends to produce values that differ from the true value
D)a bias on the part of the researcher towards those who chose not to participate in a survey
E)None of these describes nonresponse bias.

Question 32

Which of the following statistical studies is an observational study? ​

A)A group of students is surveyed to determine the percentage who believe in reincarnation.
B)A random sample of students is shown a documentary on the evolution of reincarnation beliefs throughout human history.A second random sample is not shown the documentary.The object of the study is to determine whether viewing the documentary affects belief in reincarnation.
C)To determine whether Vitamin C has any effectiveness at lessening the duration of the common cold, one set of cold sufferers is given no Vitamin C, a second set is given 2 grams per day, and a third set is given 5 grams of Vitamin C per day.
D)All of these studies are observational.
E)None of these studies is observational.

Question 33

Bias is a serious problem that sometimes arises when one takes a sample.
(a)In a few sentences, explain generally what bias is.
(b)What is the distinction between response bias and non-response bias?

Question 34

The following paragraph describes an actual study. After reading the description, determine whether the study is an observational study or an experiment. Justify your answer with specific references to the information in the study.
​
"We compared paired daytime and night counts of wild brook trout, brown trout, and rainbow trout made by the same snorkelers in five streams during August 1994. Overall, we counted 109 trout in the daytime and 333 trout at night. We speculate that trout counted at night were present during the daytime but were hidden from view. Biologists should consider that trout behavior and susceptibility to being seen might vary a great deal between daytime and night, even during summer. In some streams, the majority of trout may not be seen during the daytime."

Question 35

A study is commissioned to determine whether piglets gain body mass more rapidly when a certain hormone is introduced into their feed. In January, a random sample of 40 10-week-old piglets receives a diet that includes the hormone. Sixteen weeks later, the average weight increase is determined. A similar experiment is conducted the following June with a random sample of 36 piglets, except the hormone is removed from the diet. ​
Which of the following do you think represents the most serious flaw in this study?
​

A)the presence of a confounding variable
B)the presence of a sampling bias
C)an absence of experimental control
D)the presence of a measurement bias
E)inadequate information regarding dietary needs of piglets

Question 36

Replicating in an experiment means that the number of subjects is greater than 1.

Question 37

Which of the following best describes the meaning of "variable confounding"? ​

A)A variable is confounding if it complicates the researcher's analysis .
B)A variable is confounding if it influences the data.
C)Two variables are confounded if their effects on the response variable cannot be distinguished.
D)A variable is confounding if it influences other variables.
E)A variable is confounding when it has no influence over the data.

Question 38

A researcher wishes to study the relationship between the level of background noise and mental concentration. The treatment (noise level) will have three levels: no noise, low-intensity noise, and high-intensity noise. the subjects are to be divided into three groups, and each group is to receive one of the treatments. He has available to him a set of 60 female volunteers and a set of 90 male volunteers. What experimental design strategy would help him eliminate the introduction of gender as a confounding variable? ​

A)stratified sampling
B)replication
C)blocking
D)systematic sampling
E)double-blind trials

Question 39

A friend of yours, who is not taking statistics, wonders why it is that anyone would choose to take a sample. "Obviously," she says, "you would get better information from a census." In a short paragraph, explain why it is that statisticians take samples rather than taking a census.

Question 40

Which of the following statements is false? ​

A)The explanatory variables are those variables that have values that are controlled by the experimenter.
B)The response variable is the variable that the experimenter thinks may be affected by the explanatory variables.
C)An experimental unit is the smallest entity to which a treatment is applied.
D)Two variables are confounded if their effects on the response variable can be distinguished.
E)An experiment in which experimental units are randomly assigned to treatments is called a completely randomized experiment.

Question 41

Three methods for random sampling are: (a) simple random sampling, (b) stratified random sampling, and (c) cluster sampling. In a few sentences, discuss the similarities and differences among these sampling methods. Specifically, what sampling circumstances would lead you to choose each of these methods?

Question 42

In evaluating an experiment, how would you determine if a variable is an explanatory variable or an extraneous variable?

Question 43

Suppose that two experiments were conducted to compare the effects of two new insect repellants. In Experiment X, a simple random sample was taken from the population of River City, and the citizens were randomly assigned to repellant A and repellant B. In Experiment Y, a stratified random sample was taken from the population of River City, and the citizens were randomly assigned to repellant A and repellant B. (River City has 4 geographic areas of town, the NE, NW, SE, and SW quadrants; 100 people from each quadrant were sampled for Experiment B.)The results of the experiments were the same: fewer insects landed on the arms that had been treated with insect repellant A.
(a)For each experiment, X and Y, discuss whether one can legitimately infer from each of these experiments that repellant A is better than B? Why or why not?
(b)For each experiment, X and Y, discuss whether one can legitimately generalize to the population of River City from each of these experiments? Why or why not?

Question 44

The likelihood that an animal will successfully avoid a predator's attack should increase if the presence of the predator is detected. Animals are, of course, known to warn others of a predator's presence--the well-known prairie-dog warning call is an example. Some aquatic animals are known to send chemical signals. For example the crayfish and Iowa darter may excrete ammonium from their gills or possibly in their urine during periods of heightened metabolic activity. In an experiment to see if red-legged frogs (Rana aurora) may send or respond to chemical signals, specimens in Oregon were collected as embryos and raised in an aquarium. As tadpoles they were separated into two pairs of aquaria. The "upper tank" in each pair was connected to the "lower tank" to create a (very!) small river. A wooden heron model was placed in one of the upper tanks and moved around for 30 seconds to simulate a predator attack. Both the sender (upper tank) and receiver (lower tank) animals were monitored for added activity (increased movement) indicating antipredator behavior.
(a)What is the explanatory variable (factor) for this experiment?
(b)What is the response variable for this experiment?
(c)During the course of the experiment the investigators were very careful with the wooden heron model not to come in contact with the glass of the aquaria or make noise in any other way. If they had been unsuccessful and their wooden heron made significant amounts of noise, how would that affect the interpretation of the results?

Question 45

Two hundred people who live in San Francisco volunteered to participate in a statistical study. The volunteers were divided into two groups by age, with people under 40 years old in group 1 and people 40 years of age and older in group 2. Those in group 1 were asked to go in for sports once a day for 1 month. Those in group 2 were asked not to go in for sports for 1 month. At the end of the month, progress in weight reduction was significantly higher for group 1 than for group 2. From the resulting data, the researchers concluded that daily sports exercises help every San Francisco resident lose weight faster. Based on the study design, do you think that the conclusions are reasonable?

A)The conclusions are reasonable because this was an experiment.
B)The conclusions are not reasonable because this was not an experiment with random assignment of subjects to experimental groups.
C)The conclusions are not reasonable because this was an observational study.
D)The conclusions are reasonable because this was an experiment with random assignment of subjects to experimental groups.
E)The conclusions are not reasonable because only volunteers participated in the study.

Question 46

Fifty-five people volunteered to participate in a statistical study. For each volunteer, a coin was tossed. If the coin landed tails up, the volunteer was assigned to group 1. If the coin landed heads up, the volunteer was assigned to group 2. Those in group 1 were asked to eat carrot salad daily for 1 year. Those in group 2 were asked not to eat carrot salad for 1 year. At the end of the year, the progress in improving vision was significantly higher for group 1 than for group 2. Did the study use a random selection from some population? Did the study use random assignment to experimental groups? ​

A)The study used random selection and random assignment.
B)The study did not use random selection and random assignment.
C)The study used random selection but did not use random assignment.
D)The study used random assignment but did not use random selection.

Question 47

In competitive sports, video recorders have been used more frequently in recent years. The idea behind the recorder is that coaches can replay training sessions for more effective feedback to the athlete. Some people believe video recording may make the athletes more nervous and actually decrease their performance. You have been asked to design an experiment to address this issue for competitive high school tennis players. You have decided to use the accuracy of tennis serves as your response variable, and the number of successful serves out of 100 as your performance measure. The subjects for your experiment are 60 high school male competitive tennis players of varying ability who have volunteered for the experiment.
(a)Describe the treatments in your experiment
(b)One possible confounding variable is the experience levels of the players. Explain how you would control this variable?
(c)Can the results of this experiment be generalized to all male tennis players? Why or why not?

Question 48

One of the tasks of wildlife biologists is to estimate bird populations. One method for doing this is to walk a "transect," typically a long randomly selected rectangle, and count the number of particular species that are seen. During hunting season the biologists wear brightly colored clothes as a protective measure. A theory, known as the "species-confidence hypothesis," predicts that birds may react to these brightly colored clothes. A robin, for example, when confronted with a biologist wearing an orange color may be less afraid than if the biologist were wearing a brown color. The idea is that the orange color gives the robin some "confidence" that the biologist is another (really big!) bird. This is a difficulty because a robin that is less afraid of the biologist may be easier to see and therefore "count" because the robin lets the biologist get closer. This would result in too high an estimate of the robin population. To test this theory a biologist performed a study in her area, wearing a bright orange vest or a brown vest while working. After training herself to accurately estimate distances she indicated on her notes how close the robins would let her get before they flew away (the "approach distance"), using this as a measure of their "confidence." She randomly selected her starting points in each trip through the transects and also carefully noted the weather conditions, specifically the wind speed.
(a)What is the explanatory variable (factor) for this experiment?
(b)What is the response variable for this experiment?
(c)After completing the study the biologist was examining her results and noticed that on those days she wore the brightly-colored vest the wind tended to be of greater velocity. How does this information affect the interpretation of the results of the experiment?

Question 49

One hundred fifty people who live in Houston volunteered to participate in a statistical study. The volunteers were divided into two groups, with people who have children in group 1 and people who do not have children in group 2. Those in group 1 were asked to eat a lemon slice daily for five months. Those in group 2 were asked not to eat a lemon for five months. At the end of the study it was found that on average, people in group 1 were sick less often than those in group 2. Did the study use a random selection from some population? Did the study use random assignment to experimental groups?

A)The study used random selection and random assignment.
B)The study did not use random selection and random assignment.
C)The study used random selection but did not use random assignment.
D)The study used random assignment but did not use random selection.

Question 50

Suppose you want to know how many times per month people of Portland go shopping. You interviewed fifty women from Portland selected randomly. Is the sample likely to be representative of the population of interest?

A)No, since sample size too small.
B)Yes, since every individual in the population has an equal chance of being selected into the sample.
C)No, since you did not interview people from other cities.
D)Yes, since only women go shopping.
E)No, since not every individual in the population has an equal chance of being selected into the sample.

Question 51

Suppose you want to learn how often students of the Faculty of Arts and Sciences of Harvard University visit the gym. You interviewed students of this faculty with an athletic build. Is the sample likely to be representative of the population of interest? ​

A)Yes, since every individual in the population has an equal chance of being selected into the sample.
B)No, since only students with an athletic build visit the gym.
C)No, since you did not interview students of other faculties.
D)No, since not every individual in the population has an equal chance of being selected into the sample.
E)Yes, since the sample of students with an athletic build is representative of the population of students who visit the gym.

Question 52

The two paragraphs below discuss aspects of two studies, each of which exhibit a bias. For each study, decide whether the problem is selection bias, response bias, or nonresponse bias, and in a few sentences explain why you chose your answer.
(a)One part of the Nurses' Health Study is concerned with possible causes of skin cancer. Nurses were asked about different behaviors and aspects of their health when they entered the study. Then, the nurses were given the questionnaire again if they were diagnosed with cancer. When the questionnaires were analyzed, the investigators discovered that after the nurses were diagnosed with cancer they tended to report a reduced ability to tan. It is thought that the shift in reporting might be caused by an awareness of their diagnosis.
(b)One part of the Demographic and Health Surveys Program is concerned with measures of malnutrition. Investigators measure physical aspects of growing children, and attempt to document the physical characteristics of a population at different ages. Sadly, in some countries many children die early, and thus a bias is introduced in the study when the investigators can not collect the data from the deceased children.

Question 53

A common practice of teachers is to have students exchange their quizzes and grade each others. In addition to decreasing the teacher's work load, the reduced time between quiz and feedback is thought to be a plus for learning. Your U.S. History teacher, aware of your statistical prowess, has asked you to design an experiment to test this theory. You have decided to use the mid-term exam (not graded by students) as your response measure. Your history teacher has three classes, one early in the morning, one at noon, and one late in the afternoon. Each class contains 30 students.
(a)Describe the treatments you will use in your experiment
(b)One possible confounding variable is the time of day, since students may be more alert at certain times of the day than at other times. Describe a method would you use to control this variable? (Unfortunately you cannot change the student schedules!)(c)Do you feel the results of your experiment could be generalized to your statistics class? Why or why not?

Question 54

A pharmaceutical company wants to test its new drug that is designed to help balding men grow more hair. From their records of past customers, the company has data on about 5,000 men. The data contains information about the men's hair color, age, and percent of baldness. (A partial list is given below.) For their anticipated experiment, they want to take a sample that is representative of their customers. ​
(a)Briefly describe how you would select a simple random sample of size n = 20 from this list of customers.
(b)Describe in a short paragraph why you might wish to use a stratified random sample.

Question 55

Suppose that two experiments were conducted to assess the effect of a new insect repellant. In Experiment A, a simple random sample was taken from the population of River City. In Experiment B, a simple random sample from a group of volunteers from the population of River City was used. The results of the experiments were the same: fewer insects landed on the arms that had been treated with the insect repellant. The volunteers were randomly assigned to the two treatments in both experiments.
(a)For each experiment, A and B, discuss whether one can legitimately infer a cause-and-effect relation between the use of the repellant and fewer insects landing from each of these experiments? Why or why not?
(b)For each experiment, A and B, discuss whether one can legitimately generalize to the population of River City from each of these experiments? Why or why not?

Question 56

In evaluating an experiment, how would you determine if a variable is an explanatory variable or a response variable?