stats chapter 3
A marketing research firm wishes to determine if the adult men in Laramie, Wyoming, would be interested in a new upscale men's clothing store. From a list of all residential addresses in Laramie, the firm selects a simple random sample of 100 and mails a brief questionnaire to each. What is the population of interest?
All adult men in Laramie, Wyoming.
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 of five participants was put on a diet low in sugar and the second group of the remaining seven participants received 10% of their calories from sugar. After 8 weeks, weight gain was recorded from each participant. Which of the following basic principles of statistical design was not used in this experiment?
Blinding
You want to test the effects of water aerobics on resting heart rate. You decide to test two different levels of exercise (water aerobics for 30 minutes twice a week and water aerobics for 60 minutes once per week.) You randomly find a group of 60 (30 men and 30 women) subjects for this study. What is an appropriate blocking variable for this study?
Gender
A group of college students believes that herbal tea has remarkable restorative powers. To test its theory, the group makes weekly visits to a local nursing home, visiting with residents, talking with them, and serving them herbal tea. After several months, many of the residents are more cheerful and healthy. What is the explanatory variable in this experiment?
Herbal tea
Ann Landers once asked her female readers whether they would be content with affectionate treatment from men, with no sex ever. Over 90,000 women wrote in, with 72% answering "Yes." Why shouldn't we believe the results of this "poll?"
It was voluntary response.
Do people prefer tap or bottle water? For this study, pour two water samples into two cups that are the same but marked on the bottom. Each subject then tastes both water samples and rates the taste on a 5 point scale (1 = poor to 5 = excellent.) What type of design is this?
Matched-pairs design
Does giving an incentive really work on improving exam scores? For example, consider the following treatments to measure the use of incentives: If a block design were used, what would be an appropriate blocking variable for this study?
None of the above
A market research firm has been asked to survey the population of people in a particular city who are 16 years of age or over with respect to their preferences for television programming. To do this the firm divides the list of the target population into five age groups: 16 to 25, 26 to 35, 36 to 45, 46 to 55, and 56 or older. From each of these age groups a simple random sample of 225 people is selected for a total sample of size 1125 individuals. Assume that all of these selected individuals respond honestly to the survey questions. The resulting sample is an example of what kind of sample design?
Stratified random sample design.
Researchers wish to determine if a new experimental medication will reduce the symptoms of allergy sufferers without the side effect of drowsiness. To investigate this question, the researchers gave the new medication to 50 adult volunteers who suffer from allergies. Forty-four of these volunteers reported a significant reduction in their allergy symptoms without any drowsiness. What are the experimental units in this study?
The 50 adult volunteers.
The head of the quality control department at a publishing company is studying the effect of type of glue and type of binding on the strength of the bookbinding. The company has three possible glues to choose from and the book can either be bound as a paperback or a hardback. What should the company do if repetition is to be part of this study?
The company should use multiple books of the same binding type for each of the three types of glue
Sickle-cell disease is a painful disorder of the red blood cells that in the United States affects mostly African-Americans. To investigate whether the drug hydroxyurea can reduce the pain associated with sickle-cell disease, a study by the National Institutes of Health gave the drug to 150 sickle-cell sufferers and a placebo to another 150. The researchers then counted the number of episodes of pain reported by each subject. What is the response variable in this study?
The number of episodes of pain
A call-in poll conducted by USA Today concluded that Americans love Donald Trump. This conclusion was based on data collected from 7800 calls made by USA Today readers. USA Today later reported that 5640 of the 7800 calls for the poll came from the offices owned by one man, Cincinnati financier Carl Lindner, who is a friend of Donald Trump. What can we conclude about the results of this poll?
They are biased overstating the popularity of Donald Trump
Suppose several of the units selected into a random sample cannot be found or contacted during the conducting of a survey. What can we say about this situation?
This will likely produce nonresponse bias in the sample results.
In conducting a randomized comparative experiment, an experimenter will often include a group of subjects, known as a control group, to receive a fake treatment. What is (are) the reason(s) such a control group might be included in the experiment?
To enable the experimenter to control the effects of outside variables, such as lurking variables, on the outcome of the experiment.
To investigate whether or not sending text messages while driving impacts driving ability, we have 100 participants (50 men and 50 women) drive an obstacle course under one of the following conditions: 1) No texting while driving, 2) Sending five text messages while driving, or 3) Sending 10 text messages while driving. We measure the accuracy the subjects drove the obstacle course from a scale of 1 to 10 (1= poor and 10= excellent). Why is a control necessary in this experiment?
To help control for the lurking variables
The head of the quality control department at a publishing company is studying the effect of type of glue and type of binding on the strength of the bookbinding. The company has three possible glues to choose from and the book can either be bound as a paperback or a hardback. What is/are the factor(s) in this study?
Type of glue and type of binding
A television station is interested in predicting whether or not voters in its listening area are in favor of federal funding for abortions. It asks its viewers to phone in and indicate whether they are in favor of or opposed to this. Of the 2241 viewers who phoned in, 1574 (70.24%) were opposed to federal funding for abortions. What type of sampling method was used to collect the data?
Voluntary response
A call-in poll conducted by USA Today concluded that Americans love Donald Trump. This conclusion was based on data collected from 7800 calls made by USA Today readers. What sampling technique is being used?
Volunteer sampling
One hundred volunteers who suffer from severe depression are available for a study. Fifty are selected at random and are given a new drug that is thought to be particularly effective in treating severe depression. The other 50 are given an existing drug for treating severe depression. A psychiatrist evaluates the symptoms of all volunteers after four weeks in order to determine if there has been substantial improvement in the severity of the depression. What is the explanatory variable or factor in this study?
Which drug the volunteers receive
To investigate whether or not sending text messages while driving impacts driving ability, we have 100 participants (50 men and 50 women) drive an obstacle course under one of the following conditions: 1) No texting while driving, 2) Sending five text messages while driving, or 3) Sending 10 text messages while driving. We measure the accuracy the subjects drove the obstacle course from a scale of 1 to 10 (1= poor and 10= excellent). What is a possible lurking variable in this experiment?
driving skill level
A sociologist wants to study the attitudes of American male college students toward marriage and husband-wife relations. She gives a questionnaire to 25 of the men enrolled in Sociology 101 at her college. All 25 complete and return the questionnaire. The sample in this situation is
the 25 men who received and returned the questionnaire
Answer True or False to the following questions:
true true true false
Which of the following should a researcher be concerned about when conducting a sample survey?
all of the above
In order to assess the opinion of students at the University of Montana on campus snow removal, a reporter for the student newspaper interviews the first 12 students he meets who are willing to express their opinion. In this case, the population is
all students at the University of Montana
A researcher is studying the effects of a new drug on reducing high blood pressure. He recruits 250 men to test the new active drug against a current standard. At the end of six weeks, the decrease in systolic blood pressure will be evaluated. He believes the drug will be more effective for black men than for white men. To properly test his belief, the experiment should be
blocked.
To investigate whether or not sending text messages while driving impacts driving ability, we have 100 participants (50 men and 50 women) drive an obstacle course under one of the following conditions: 1) No texting while driving, 2) Sending five text messages while driving, or 3) Sending 10 text messages while driving. We measure the accuracy the subjects drove the obstacle course from a scale of 1 to 10 (1= poor and 10= excellent). We are testing the effect of sending text messages at three different
levels
The administration at a large state university is interested in getting the opinions of students on a proposed instructional fee for use of computer labs on campus. They select a simple random sample of 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors. This is an example of
stratified random sample
A statistics instructor wants to know which route will get her to school the fastest. Each day from October 2 to November 15, when she gets to the turn point she checks the odometer on her car. If it shows an even number she takes the freeway; if it shows an odd number, she takes the in-town route. She records the total time each day. What is the explanatory variable in this study?
the route
A statistics instructor wants to know which route will get her to school the fastest. Each day from October 2 to November 15, when she gets to the turn point she checks the odometer on her car. If it shows an even number she takes the freeway; if it shows an odd number, she takes the in-town route. She records the total time each day. What is the response variable in this study?
the time to school
Suppose you want to determine if there are differences in the average prices among items at three local supermarket chains. If a block design were used, what would be an appropriate blocking variable for this study?
type of item
A market research company wishes to find out whether the population of students at a university prefers brand A or brand B of instant coffee. A random sample of students is selected, and each one is asked to try first brand A and then brand B, or vice versa (with the order determined at random). They then indicate which brand they prefer. The response variable is
which brand they prefer
To investigate whether or not sending text messages while driving impacts driving ability, we have 100 participants (50 men and 50 women) drive an obstacle course under one of the following conditions: 1) No texting while driving, 2) Sending five text messages while driving, or 3) Sending 10 text messages while driving. We measure the accuracy the subjects drove the obstacle course from a scale of 1 to 10 (1= poor and 10= excellent). What kind of study is this?
Experiment
David A. Miller owns a small advertising business. He has nine employees. The names of the employees are given below: Determine whether each of the following statements is true or false.
If we used another list of random digits to select the sample, we would get a completely different sample than that obtained with the list actually used. FALSE If we used another list of random digits to select the sample, we would get the same result as obtained with the list actually used. FALSE If we used another list of random digits to select the sample, the result obtained with the list actually used would be just as likely to be selected as any other set of three names. TRUE
To investigate whether or not sending text messages while driving impacts driving ability, we have 100 participants (50 men and 50 women) drive an obstacle course under one of the following conditions: 1) No texting while driving, 2) Sending five text messages while driving, or 3) Sending 10 text messages while driving. We measure the accuracy the subjects drove the obstacle course from a scale of 1 to 10 (1= poor and 10= excellent). What is the treatment in this study?
Number of text messages sent while driving
The head of the quality control department at a publishing company is studying the effect of type of glue and type of binding on the strength of the bookbinding. The company has three possible glues to choose from and the book can either be bound as a paperback or a hardback. How many treatments is the company considering?
6
One hundred volunteers who suffer from severe depression are available for a study. Fifty are selected at random and are given a new drug that is thought to be particularly effective in treating severe depression. The other 50 are given an existing drug for treating severe depression. A psychiatrist evaluates the symptoms of all volunteers after four weeks in order to determine if there has been substantial improvement in the severity of the depression. Suppose volunteers were first divided by gender, and then half of the men were randomly assigned to the new drug and half of the women were assigned to the new drug. The remaining volunteers received the other drug. What is this an example of?
A block design
In order to select a sample of undergraduate students in the United States, a simple random sample of four states is selected. From each of these states, a simple random sample of two colleges or universities is then selected. Finally, from each of these eight colleges or universities, a simple random sample of 20 undergraduates is selected. The final sample consists of 160 undergraduates. What sampling technique is being used?
Multistage sampling
You want to test the effects of water aerobics on resting heart rate. You decide to test two different levels of exercise (water aerobics for 30 minutes twice a week and water aerobics for 60 minutes once per week.) You randomly find a group of 60 (30 men and 30 women) subjects for this study. Which of the following was used in this experiment?
None of the above
A simple random sample of 50 students will be taken from a local community college, which has a total of about 1500 students. Another simple random sample of 50 students will be taken from a large state university, which has a total of approximately 20,000 students. The sampled students will each answer a one-question survey which reads: "About how many DVDs do you own?" The sample average number of DVDs owned will be calculated for the two sets of students. What sampling technique is being used to here?
Stratified random sampling
The head of the quality control department at a publishing company is studying the effect of type of glue and type of binding on the strength of the bookbinding. The company has three possible glues to choose from and the book can either be bound as a paperback or a hardback. Many stacks of books are ready to be bound—some in paperback form, some in hardback form. As part of this study, 45 books are to be randomly selected from each type of binding, and then randomly assigned to one of the three types of glue. What type of sampling method is being used to select the books?
Stratified sample
A medicine to remove the redness in eyes was tested in a group of 100 students. Each student took either the medicine or a placebo in both eyes. The specific treatment for each student was decided by flipping a coin. The participants in the study did not know if heads or tails resulted in the medication. For each of the following basic principles of statistical design, indicate if it was used in this experiment or not.
all yes
Two amateur gardeners are interested in comparing the yields of two varieties of tomatoes. They each have small backyard gardens. Each gardener is going to plant three plants of each variety in his garden. The first gardener will select six small areas in his garden for planting, then choose three of these at random for the three plants of the first variety and then use the remaining three for the second variety. The second gardener will follow the same procedure with his own randomization in his garden. At the end of the growing season they will compare the yields of the two varieties. In this example the gardens are
blocks
You want to test the effects of water aerobics on resting heart rate. You decide to test two different levels of exercise (water aerobics for 30 minutes twice a week and water aerobics for 60 minutes once per week.) You randomly find a group of 60 (30 men and 30 women) subjects for this study. The treatment in this experiment is
exercise
Twelve people, who suffer from chronic fatigue syndrome, volunteer to take part in an experiment to see if shark fin extract will increase one's energy level. Eight of the volunteers are men and four are women. Half of the volunteers are to be given shark fin extract twice a day and the other half a placebo twice a day. We wish to make sure that four men and two women are assigned to each of the treatments, so we decide to use a block design with the men forming one block and the women the other. Suppose one of the researchers is responsible for measuring if a subject displays an increase in energy level. What design principle should be added to this experiment?
Conduct the study as a double-blind experiment.
In order to determine if smoking causes cancer, researchers surveyed a large sample of adults. For each adult they recorded whether the person had smoked regularly at any period in their life and whether the person had cancer. They then compared the proportion of cancer cases in those who had smoked regularly at some time in their lives with the proportion of cases in those who had never smoked regularly at any point in their lives. The researchers found a higher proportion of cancer cases among those who had smoked regularly than among those who had never smoked regularly. What type of study is this?
An observational study
Suppose you want to determine if there are differences in the average prices among items at three local supermarket chains. What type of study would work best?
An observational study
A baseball enthusiast believes pitchers who strike out a lot of batters also walk a lot of batters. He reached this conclusion by going to the library and examining the records of all major league pitchers between 1990 and 1995. What type of study is his decision based on?
An observational study based on available data
An amateur gardener decides to change the variety of tomatoes for this year to see if the yield improves. He put in six plants the previous year and six plants this year using the same part of the garden. The average yield per plant was 11.3 pounds per plant in the previous year and 14.5 pounds per plant using the new variety. What is this an example of?
An observational study, not an experiment
In order to assess the effects of exercise on reducing cholesterol, a researcher sampled 50 people from a local gym who exercise regularly and 50 people from the surrounding community who, were assumed, do not exercise regularly. Each subject reported to a clinic to have their cholesterol measured. The subjects were unaware of the purpose of the study, and the technician measuring the cholesterol was not aware of whether the subject exercises regularly or not. What type of study is this?
An observational study.
Do people prefer tap or bottle water? For this study, pour two water samples into two cups that are the same but marked on the bottom. Each subject then tastes both water samples and rates the taste on a 5 point scale (1 = poor to 5 = excellent.) In order to make the experiment easier to conduct, you decide to pour the tap water into red cups and the bottled water into blue cups. Which of the following statements correctly identifies what is wrong with this plan?
The cup color may bias the experiment by making subjects choose the color they prefer over the taste Subjects may notice that all the red cups are bottled (or tap)
A marketing research firm wishes to determine if the adult men in Laramie, Wyoming, would be interested in a new upscale men's clothing store. From a list of all residential addresses in Laramie, the firm selects a simple random sample of 100 and mails a brief questionnaire to each. What do we know about the chance that all 100 homes in a particular neighborhood in Laramie end up being the sample of residential addresses that is selected?
t is the same as for any other set of 100 residential addresses
In order to be able to select a simple random sample to carry out a survey, it is necessary to define carefully the population from which information is desired and to have a list of all the members of that population. The list, from which the sample is actually selected, called the sampling frame, may not be a complete listing of the members of the population. In this case the survey will be said to suffer from
undercoverage bias
A study was conducted to determine the effect of weather on varieties of corn grown for grazing by cattle in Alberta, Canada. To conduct the study, five varieties of corn were considered (one grazing, one short-stature, and three conventional) with harvesting of crops conducted on four occasions (two dates in September, one in December, and one in January). The experimental treatments were assigned at random to plots of land at each of two different locations in Alberta in order to control for natural variations in location. The crude protein concentration of the harvested corn was determined. The two Alberta locations used in the study were Lacombe and Brooks. In this study Location is considered to be what kind of variable?
A blocking variable
An opinion poll is to be given to a sample of 90 members of a local gym. The members are first divided into men and women, and then a simple random sample of 45 men and a separate simple random sample of 45 women are taken. What is this is an example of?
A stratified random sample
A large university wishes to determine the percentage of its students that have committed some form of academic dishonesty, such as cheating on an examination or plagiarism on assignments during their academic career. To determine the desired percentage, a random sample of their current students is selected. Each selected student is then interviewed by a staff member and asked if they had cheated. The results of this survey likely will be unreliable because
All of the above are reasons for concern
A survey interviews 1000 Americans by telephone and asks "What do you think is the biggest problem facing education today?" The population of interest for this poll is most likely
American adults
Does giving an incentive really work on improving exam scores? For example, consider the following treatments to measure the use of incentives: What type of study would work best?
An experiment
Olivia is planning to take a foreign language class. To research how satisfied other students are with their foreign language classes, she decides to take a sample of 20 such students. The university offers classes in four languages: Spanish, German, French, and Japanese. She will select a simple random sample of five students from each language. Olivia asks the instructors of the 20 selected students to have the students rate the class they are currently enrolled in. If Olivia plans to use these ratings to learn about how satisfied all foreign language students are, why will the results be questionable?
Because of response bias
Seventy-five college students are taking part in a study initiated by a large computer manufacturer. The company is designing a new type of laptop computer and has created prototypes of it with two different keyboard designs. They are also including the current design of the laptop in the experiment. Each of the students was randomly assigned to one of the three types of computers. The students are asked to spend 15 minutes on one of the computers performing several tasks (typing words, numbers, making corrections, etc.). The ease of use of the keyboard was then rated on a five-point scale by having the students fill out a short questionnaire. Which of the following basic principles of statistical design was not used in this experiment?
Blinding
A study was conducted with the object of determining the effect on blood pressure and cholesterol levels in women over the age of 60 of two different strength-training programs, one involving the use of a balance ball and the other using stationary exercise equipment. Eighty women over the age of 60 were identified and randomly divided into two equal-sized experimental groups. Each member of the two groups was trained and allowed to follow the prescribed routine for eight weeks. The subjects were aware of the purpose of the study but not that there were two different treatment groups involved. The cholesterol levels and blood pressure for subjects were measured at the start and at the end of the eight weeks. The experimenter and the medical technician were not told to which group any of the subjects were assigned. This is an example of an attempt to conduct
a double-blind randomized experiment.
There are four people in a family-a father, a mother and two children-and they have won two tickets to go to Disneyland for a week. They decide to select a sample of two people for the trip as follows: The mother and father flip a coin to see which of the two of them will go, and they then flip a coin to see which of the two children will go. This is
a probability sample from the family since each member of the family has a known chance of being selected to go on the trip
A small college has 500 Freshmen, 400 Sophomores, 350 Juniors, and 300 Seniors. They wish to conduct a survey of their students and find a simple random sample of 50 Freshmen, 40 Sophomores, 35 Juniors, and 30 Seniors. The overall sample is
a stratified sample
A study sponsored by American Express Co. and the French government tourist office found that old American stereotypes about French unfriendliness weren't true. The respondents were more than 1,000 Americans who have visited France more than once for pleasure over the past two years. The results of this study are probably
biased, overstating the extent to which the old stereotypes weren't true
A simple random sample of 1200 adult Americans is selected and each person is asked the following question: "In light of the huge national deficit, should the government at this time spend additional money to establish a national system of health insurance?" Only 39% of those responding answered yes. Determine whether each of the following statements regarding this survey is true or false.
false false false true
