MTH245
You want to determine the opinions of students regarding stem cell research. Identify the sampling technique you are using when you select these samples. 1. You select a class at random and question each student in the class. 2. You assign each student a number and, after choosing a starting number, question every 25th student.
(1) This is cluster sampling. The sample was selected by using the students in a randomly chosen class. (2) This is systematic sampling. The sample was selected by numbering each student in the school, randomly choosing a starting number, and selecting students at regular intervals from the starting number.
Researchers in Germany tested the effect of a dietary supplement designed to control metabolism in patients with type 2 diabetes. Thirty-one patients with type 2 diabetes completed the study. The patients were assigned at random either the supplement or a placebo for 12 weeks. After a subsequent "wash-out" period of 12 weeks, the patients were assigned the other product. At the conclusion of the study, the patients' glycated hemoglobin, fasting blood glucose, and fructosamine levels were checked, as well as their lipid parameters.. (a) Identify the experimental units and treatments used in this experiment. (b) Identify a potential problem with the experimental design being used and suggest a way to improve it. (c) The experiment is described as a placebo-controlled, double-blind study. Explain what this means. (d) How could blocking be used in designing this experiment?
(a)The experimental units are the 31 patients with type 2 diabetes. The treatment is a dietary supplement designed to control metabolism in patients with type 2 diabetes. (b) A problem with the design is that the sample size is small. The experiment could be replicated to increase validity. (c) In a placebo-controlled, double-blind experiment, neither the subject nor the experimenter knows whether the subject is receiving a treatment or a placebo. The experimenter is informed after all the data have been collected. (d) Divide the subjects into age categories and then, within each age group, randomly assign subjects to either the treatment group or the control group.
A pharmaceutical company wants to test the effectiveness of a new drug used to treat migraine偏頭痛 headaches. The company identifies 500 females ages 25 to 45 years old who suffer from migraine headaches. The subjects are randomly assigned into two groups. One group is given the drug and the other is given a placebo that looks exactly like the drug. After three months, the subjects' symptoms are studied and compared. (a) Identify the experimental units and treatments used in this experiment. (b) Identify a potential problem with the experimental design being used and suggest a way to improve it. (c) How could this experiment be designed to be double-blind?
(a)The experimental units are the 500 females ages 25 to 45 years old who suffer from migraine headaches. The treatment is the new drug used to treat migraine headaches. (b) A problem with the design is that the sample is not representative of the entire population because only females ages 25 to 45 were used. To increase validity, use a stratified sample. (c) For the experiment to be double-blind, neither the subjects nor the company would know whether the subjects are receiving the drug or the placebo.
A researcher wants to study the effects of sleep deprivation on motor skills. Eighteen people volunteer for the experiment: Jake, Maria, Mike, Lucy, Ron, Adam, Bridget, Carlos, Steve, Susan, Vanessa, Rick, Dan, Kate, Pete, Judy, Mary, and Connie. Use a random number generator to choose nine subjects for the treatment group. The other nine subjects will go into the control group. List the subjects in each group. Tell which method you used to generate the random numbers.
(d) Divide the subjects into age categories and then, within each age group, randomly assign subjects to either the treatment group or the control group.
Identify the sampling technique used, and discuss potential sources of bias (if any). Explain. You want to know the favorite spring break destination among 15,000 students at a university. Determine whether you would take a census or use a sampling. If you would use a sampling, determine which sampling technique you would use. Explain your reasoning.
. Sample answer: Sampling, because the population of students at the university is too large for their favorite spring break destinations to be easily recorded. Random sampling would be advised because it would be easy to select students randomly and then record their favorite spring break destination.
What is the difference between a census and a sampling?
A census includes the entire population; a sampling includes only a portion of the population.
Volunteers for an experiment are numbered from 1 to 90. The volunteers are to be randomly assigned to two different treatment groups. Use a random number generator different from the one you used in Exercise 21 to choose 45 subjects for the treatment group. The other 45 subjects will go into the control group. List the subjects, according to number, in each group. Tell which method you used to generate the random numbers.
Answers will vary. Sample answer: Using a random number generator:Treatment group: 1,2,3,4,5,6,7,9,12,15,18,20,22,23,26,27,28,30,31,32,33,34,35,36,37,38,41,42, 44,50,54,63,68,70,73,74,78,80,81,82,85,86,87,88,89 Control group: 8,10,11,13,14,16,17,19,21,24,25,29,39,40,43,45,46,47,48,49,51,52,53,55,56,57, 58,59,60,61,62,64,65,66,67,69,71,72,75,76,77,79,83,84,90.
Determine whether each study is an observational study or an experiment. Researchers study the effect of vitamin D3 supplementation among patients with antibody deficiency or frequent respiratory tract infections. To perform the study, 70 patients receive 4000 IU of vitamin D3 daily for a year. Another group of 70 patients receive a placebo daily for one year.
Because the study applies a treatment (vitamin D3) to the subjects, the study is an experiment.
Determine whether each study is an observational study or an experiment. Researchers conduct a study to determine how confident Americans are in the U.S. economy. To perform the study, researchers call 3040 U.S. adults and ask them to rate current U.S. economic conditions and whether the U.S. economy is getting better or worse.
Because the study does not attempt to influence the responses of the subjects (there is no treatment), the study is an observational study.
Determine whether you would take a census or use a sampling. If you would use a sampling, determine which sampling technique you would use. Explain The average age of the 115 residents of a retirement community
Census, because it is relatively easy to obtain the ages of the 115 residents.
Identify the sampling technique used, and discuss potential sources of bias (if any). Explain. A study in a town in northwest Ethiopia designed to determine prevalence流行 and predictors of depression among pregnant women randomly selects four districts of the town, then interviews all pregnant women in these districts.
Cluster sampling is used because each district is considered a cluster and every pregnant woman in a selected district is surveyed. A potential source of bias is that the selected districts may not be representative of the entire area.
After a hurricane, a disaster area is divided into 200 equal grids. Thirty of the grids are selected, and every occupied household in the grid is interviewed to help focus relief efforts on what residents require the most.
Cluster sampling is used because the disaster area is divided into grids, and 30 grids are then entirely selected. A possible source of bias is that certain grids may have been much more severely damaged than others.
Identify the sampling technique used, and discuss potential sources of bias (if any). Explain. A journalist interviews 154 people waiting at an airport baggage claim and asks them how safe they feel during air travel.
Convenience sampling is used because of the convenience of surveying people waiting for their baggage. A potential source of bias is that all of the people just got off an airplane.
Identify the sampling technique used, and discuss potential sources of bias (if any). Explain. A student asks 18 friends to participate in a psychology experiment.
Convenience sampling is used because the student sampled a convenient group of friends. The study may be biased toward the opinions of the student's friends.
Questioning university students as they leave a fraternity party男子学生の友好会, a researcher asks 463 students about their study habits.
Convenience sampling is used because the students are chosen due to their convenience of location. Bias may enter into the sample because the students sampled may not be representative of the population of students.
Determine whether the study is an observational study or an experiment. To study the effects of social media on teenagers' brains, researchers showed a few dozen teenagers photographs that had varying numbers of "likes" while scanning the reactions in their brains.
Experiment. The study applies a treatment (different photographs) to the subjects.
Determine whether the study is an observational study or an experiment. Explain. Researchers conduct a study to determine whether a drug used to treat hypertension in patients with obstructive sleep apnea 無呼吸works better when taken in the morning or in the evening. To perform the study, 78 patients are given one pill to take in the morning and one pill to take in the evening (one containing the drug and the other a placebo). After 6 weeks, researchers collected blood pressure information on the patients.
Experiment. The study applies a treatment (drug to treat hypertension in patients with obstructive sleep apnea閉塞性睡眠時無呼吸) to the subjects.
Determine whether the study is an observational study or an experiment. Researchers demonstrated that adults using an intensive program to lower systolic blood pressure to less than 120 millimeters of mercury reduce the risk of death from all causes by 27%.
Experiment. The study applies a treatment (intensive program to lower systolic blood pressure) to the subjects.
True or False? A placebo is actual treatment.
False A placebo is a fake treatment.
True or False? A convenience sample is always representative of a population.
False. A convenience sample is not representative of a population.
True or False? A double-blind experiment is used to increase the placebo effect.
False. A double-blind experiment is used to decrease the placebo effect.
True or False? The method for selecting a stratified sample is to order a population in some way and then select members of the population at regular intervals.
False. To select a systematic sample, a population is ordered in some way and then members of the population are selected at regular intervals.
True or False? Using a systematic sample guarantees that members of each group within a population will be sampled.
False. Using stratified sampling guarantees that members of each group within a population will be sampled.
What is the difference between a random sample and a simple random sample?
In a random sample, every member of the population has an equal chance of being selected. In a simple random sample, every possible sample of the 「same size」 has an equal chance of being selected.
What is the difference between an observational study and an experiment?
In an experiment, a treatment is applied to part of a population and responses are observed. In an observational study, a researcher measures characteristics of interest of a part of a population but does not change existing conditions.
Determine the level of measurement of the data set. Explain The daily high temperatures(in degrees Fahrenheit)for Sacramento, California, for a week in September are listed. 90-80-76-84-91-94-97
Interval. The data can be ordered and meaningful differences can be calculated, but it does not make sense to say that 84 degrees is 1.05 times as hot as 80 degrees.
Determine the level of measurement of the data set. Explain The four departments of a printing company are listed. Administration - Sales - Production - Billing
Nominal. The data are qualitative and cannot be arranged in a meaningful order.
200 students volunteer for an experiment to test the effects of sleep deprivation 睡眠不足 on memory recall. The students will be placed in one of five different treatment groups, including the control group. Explain how you could design an experiment so that it uses a completely randomized design.
Number the volunteers and then use a random number generator to assign subjects randomly to one of the treatment groups or the control group.
Determine whether the study is an observational study or an experiment. In a survey of 1033 U.S. adults, 51% said U.S. presidents should release all medical information that might affect their ability to serve.
Observational study. The study does not apply a treatment to the adults.
Determine whether the study is an observational study or an experiment. In a study designed to research the effect of music on driving habits, 1000 motorists ages 17-25 years old were asked whether the music they listened to influenced their driving.
Observational study. The study does not apply a treatment to the motorists.
Determine whether the study is an observational study or an experiment. Explain. Researchers conducted a study to determine the effect of coffee consumption on the development of multiple sclerosis多発性硬化症. To perform the study, researchers asked 4408 adults in Sweden and 2331 adults in the United States how many cups of coffee they drink per day.
Observational study. The study does not attempt to influence the responses of the subjects and there is no treatment.
Determine the level of measurement of the data set. Explain The vehicle size classes for a sample of sedans are listed. Mini compact - Subcompact - Compact- Mid-size Large
Ordinal. The data are qualitative and could be arranged in order of car size.
Determine whether the number describes a population parameter or a sample statistic. Explain your reasoning. In a study of math majors at a university, 10 students minored in physics.
Population Parameter. The 10 students minoring in physics is a numerical description of all math majors at a university.
Determine whether the number describes a population parameter or a sample statistic. Explain your reasoning. In 2016, the National Science Foundation announced $22.7 million in infrastructure-strengthening investments.
Population parameter. The value $22.7 million is a numerical description of the total infrastructure- strengthening investments.
Identify the population and the sample. Describe the sample data set. Eighty-three doctors working in the St. Louis area were surveyed concerning their opinions of health care reform.
Population: Collection of the opinions on health care reform of all doctors in the St. Louis area Sample: Collection of the opinions on health care reform of the 83 doctors in the St. Louis area who were sampled Sample data set: Doctors in the St. Louis area and their opinions on health care reform
Identify the population and the sample. Describe the sample data set. A survey of 4787 U.S. adults found that 15% use ride-hailing applications.
Population: Collection of the responses of all U.S. adults Sample: Collection of the responses of the 4787 U.S. adults who were sampled Sample data set: 15% of adults who use ride-hailing applications and 85% who do not
Identify the population and the sample. Describe the sample data set. A survey of 1601 U.S. children and adults ages 16 years and older found that 48% have visited a public library or a bookmobile over a recent span of 12 months.
Population: Collection of the responses of all U.S. children and adults ages 16 years and older Sample: Collection of the responses of the 1601 U.S. children and adults ages 16 and older who were sampled Sample data set: 48% of children and adults who have visited a public library or a bookmobile over a recent span of 12 months and 52% who did not
Determine whether the data are qualitative or quantitative. Explain your reasoning. The marital statuses of all engineers at an electric utility
Qualitative, because marital statuses are attributes.
Determine whether the data are qualitative or quantitative. Explain your reasoning. The zip codes of a sample of 200 customers at a sporting goods store
Qualitative, because zip codes are labels for customers.
Determine whether the data are qualitative or quantitative. Explain your reasoning. The ages of a sample of 350 employees of a software company
Quantitative, because ages are numerical measurements.
Determine whether the data are qualitative or quantitative. Explain your reasoning. The revenues of the companies on the Fortune 500 list
Quantitative, because revenues are numerical measures.
The total compensations 補償金(in millions of dollars) of the ten highest-paid CEOs at U.S. public companies are listed. 94.6- 56.4 - 54.1 - 53.2 - 53.2 - 51.6 - 47.5
Ratio. The data are quantitative, and it makes sense to say that $53.2 million is 1.12 times as much as $47.5 million.
What is replication in an experiment? Why is replication important?
Replication is the repetition of an experiment under the same or similar conditions. Replication is important because it enhances the validity of the results.
Determine whether the survey question is biased. If the question is biased, suggest a better wording. Why does eating whole-grain foods improve your health?
The question is biased because it already suggests that eating whole-grain foods improves your health. The question might be rewritten as "How does eating whole-grain foods affect your health?"
Determine whether the survey question is biased. If the question is biased, suggest a better wording. Why does text messaging while driving increase the risk of a crash?
The question is biased because it already suggests that text messaging while driving increases the risk of a crash. The question might be rewritten as "Does text messaging while driving affect the risk of a crash?"
A company employs 79 people. Choose a simple random sample of five to survey.
Sample answer: Assign numbers 1 to 79 to the employees of the company. Use the table of random numbers and obtain 63, 7, 40, 19, and 26. The employees assigned these numbers will make up the sample.
Determine whether the number describes a population parameter or a sample statistic. Explain your reasoning. In a survey of 1000 likely U.S. voters, 29% trust media fact-checking of candidates' comments.
Sample statistic. The value 29% is a numerical description of a sample of U.S. voters.
Determine whether the number describes a population parameter or a sample statistic. Explain your reasoning. Thirty percent of a sample of 521 U.S. workers say that they worry about having their benefits reduced.
Sample statistic. The value 30% is a numerical description of a sample of U.S. workers.
Determine whether you would take a census or use a sampling. If you would use a sampling, determine which sampling technique you would use. Explain The most popular type of movie among 100,000 online movie rental subscribers
Sampling, because the population of subscribers is too large to easily record their favorite movie type. Random sampling would be advised because it would be easy to randomly select subscribers and then record their favorite movie types.
Selecting employees at random from an employee directory, researchers contact 300 people and ask what obstacles (such as computer problems) keep them from accomplishing tasks at work.
Simple random sampling is used because each employee has an equal chance of being contacted, and all samples of 300 people have an equal chance of being selected. A possible source of bias is that the random sample may contain a much greater percentage of employees from one department than from others.
From calls made with randomly generated telephone numbers, 1012 respondents are asked if they rent or own their residences.
Simple random sampling is used because each telephone number has an equal chance of being dialed, and all samples of 1012 phone numbers have an equal chance of being selected. The sample may be biased because telephone sampling only samples those individuals who have telephones, who are available, and who are willing to respond.
Identify the sampling technique used, and discuss potential sources of bias (if any). Explain. Using random digit dialing, researchers ask 1201 U.S. adults whether enough is being done to fight opioid addiction.
Simple random sampling is used because random telephone numbers were generated and called. A potential source of bias is that telephone sampling only samples individuals who have telephones, who are available, and who are willing to respond.
Determine whether the survey question is biased. If the question is biased, suggest a better wording. How does the media influence the opinions of voters?
The question is biased because it already suggests that the media influences the opinions of voters. The question could be rewritten as "Does the media influence the opinions of voters?"
Soybeans are planted on a 48-acre field. The field is divided into one-acre subplots. A sample is taken from each subplot to estimate the harvest.
Stratified sampling is used because a sample is taken from each one-acre subplot (stratum).
Identify the sampling technique used, and discuss potential sources of bias (if any). Explain. Twenty-five students are randomly selected from each grade level at a high school and surveyed about their study habits.
Stratified sampling is used because the population is divided by grade level and then 25 students are randomly selected from each grade level.
Every tenth person entering a mall is asked to name his or her favorite store.
Systematic sampling is used because every tenth person entering the shopping mall is sampled. It is possible for bias to enter the sample if, for some reason, there is a regular pattern to people entering the shopping mall.
Identify the sampling technique used, and discuss potential sources of bias (if any). Explain. Law enforcement officials stop and check the driver of every third vehicle for blood alcohol content.
Systematic sampling is used because every third car is stopped. A potential source of bias is that the street the law enforcement officials are using may be near a bar.
Which part of the survey described in Exercise 4 represents the descriptive branch of statistics? Make an inference based on the results of the survey. Exercise 4 )A survey of 1601 U.S. children and adults ages 16 years and older found that 48% have visited a public library or a bookmobile over a recent span of 12 months.
The statement "48% have visited a public library or a bookmobile over a recent span of 12 months" is an example of descriptive statistics. An inference drawn from the sample is that about half of U.S. children and adults ages 16 years and older have visited a public library or a bookmobile over a recent span of 12 months.
Determine whether the number describes a population parameter or a sample statistic. Explain your reasoning. Which part of the survey described in Exercise 3 represents the descriptive branch of statistics? Make an inference based on the results of the survey. Exercise 3 )A survey of 2223 U.S. adults found that 62% would encourage a child to pursue a career as a video game developer or designer
The statement "62% would encourage a child to pursue a career as a video game developer or designer" is an example of descriptive statistics. An inference drawn from the sample is that a majority of people encourage children to pursue a career as a video game developer or designer.
200 students volunteer for an experiment to test the effects of sleep deprivation 睡眠不足 on memory recall. The students will be placed in one of five different treatment groups, including the control group. Explain how you could design an experiment so that it uses a randomized block design.
The subjects could be split into male and female and then be randomly assigned to each of the five treatment groups.
Determine whether the survey question is biased. If the question is biased, suggest a better wording. How much do you exercise during an average week?
The survey question is unbiased because it does not imply how much exercise is good or bad.
Example 2：A company wants to test the effectiveness of a new gum developed to help people quit smoking. The company in Example 2 identifies 240 adults who are heavy smokers. The subjects are randomly assigned to be in a gum treatment group or in a control group. Each subject is also given a DVD featuring the dangers of smoking. After four months, most of the subjects in the treatment group have quit smoking. Identify a potential problem with the experimental design and suggest a way to improve it.
There is no way to tell why the people quit smoking. They could have quit smoking as a result of either chewing the gum or watching the DVD. The gum and the DVD could be confounding variables. To improve the study, two experiments could be done, one using the gum and the other using the DVD. Or just conduct one experiment using either the gum or the DVD.
The Pennsylvania Game Commission conducted a study to count the number of elk鹿 in Pennsylvania. The commission captured and released 636 elk, which included 350 adult cows, 125 calves, 110 branched bulls, and 51 spikes. Is this study an observational study or an experiment?
This is an observational study.
True or False? To select a cluster sample, divide a population into groups and then select all of the members in at least one (but not all) of the groups.
True