stupid statistics
A golf course has 18 holes. A guidebook provided to golfers includes useful information about each hole. The individuals in this data set are shown below. Which of the variables in the data set is a categorical variable?
difficulty level
The manufacturer of an iced tea brand is tweaking its formula and conducting a taste test to see if the original flavor or the new flavor is preferred. The tea is served to 150 taste testers in identical cups with no labels, and their preferences are recorded. The cups have "A" or "B" marked on the bottom to identify which flavor is in each cup, and they are presented in a random order so that the test administrators do not know what flavor is in each cup until after the taste tester makes their choice.
double blind
A basketball roster is shown in the table. Which variable would be classified as a continuous quantitative variable?
height
A university wants to survey students to gather opinions regarding a tuition increase for their online degree programs. Which survey method is most likely to lead to nonresponse bias in the sample?
Station interviewers at high-traffic areas near the student center to administer the survey to students trying to get to class.
A nutritionist selected a random sample of adults and asked them about their eating and exercise habits. The data show that people who eat organic fruits and vegetables are more likely to exercise regularly than those who do not eat organic fruits and vegetables. Does this scenario describe an observational study or an experiment?
observational study
When sampling, which of the following sample sizes will yield the smallest variability in results obtained from repeated sampling from the population?
35
A beauty product company conducts a study to test the effectiveness of a new shampoo to control split ends. One hundred subjects have volunteered to take part in the study, and will be split into a treatment group and a placebo group. The study leader will randomly assign the subjects to the groups using slips of paper. How many slips of paper will the researcher need to draw in order to randomly assign subjects to the treatment groups?
50
A telemarketing company is conducting a study of new calling scripts. Seventy-five employees will be randomly assigned to three new scripts using a table of random digits. The study leader will assign the subjects to the groups using a table of random digits. How many unique two-digit numbers within the range of 01 to 75 will the study designer need to select from the table?
50
Read each scenario and choose the type of bias that is exhibited.
A college professor has a colleague administer a survey to each member of his class about the effectiveness of his teaching strategies. This exhibits nonresponseX responseX undercoverage✔ no bias. At the end of a lecture, a college professor polls his lecture class of 200 students about the importance of attending his lectures. This exhibits nonresponseX response✔ undercoverageX no bias.
Read each scenario and choose the type of bias that is exhibited.
A college professor polls each student as they leave the final exam about the effectiveness of his teaching strategies. This exhibits response✔ bias. A college professor hands out a notecard the last day of class asking each student to write comments about the effectiveness of his teaching strategies. This exhibits ✔ nonresponse
A candy manufacturer is testing new brands of sugar and needs to assign 150 recipes to two treatment groups. A table of random digits will be used to generate the sample. Select the appropriate way to number the experimental units.
000-149
A school principal wants to conduct a survey of student electronic use in her high school. She wants to select an SRS of 50 from the 690 students in the school using a random number table. Which of the following are correct methods for labeling the population? Check all that apply.
000-689 001-690
Several members of a running club would like to survey the rest of the members to determine which 5K races the club should enter. They decide to use a random number table to sample 10 of the 78 members. Which of the following correctly labels the population?
01-78
A researcher needs to assign 45 subjects, numbered 01 to 45, to one of three treatment groups: A, B, or C. Use the table of random digits, starting with the first row and first column, to carry out the random assignment. Which subjects will be in group A?
29, 17, 37, 20, 45, 27, 12, 23, 26, 25, 19, 30, 11, 28, 31
A researcher is comparing the effectiveness of three devices designed to help people who snore. There are 60 people who snore participating in the experiment who are labeled 01-60. Using a table of random digits, the researcher will randomly place the participants into three equally sized treatment groups suitable for comparison. Carry out the random assignment using the given selection from a table of random digits, starting with the first row and first column. Which list assigns the first eight people to the device 1 group?
29, 17, 37, 48, 20, 27, 12, 23
An inspector selects a random sample of 25 wireless keyboards from today's production line to assess whether or not they work properly. He finds that 24 of the 25 wireless keyboards do work properly. Which of the following conclusions can we draw from this study? A: We can infer that about 96% of the wireless keyboards produced by the manufacturer that day will work properly. B: We can draw conclusions about cause and effect for the population of all wireless keyboards produced today by this manufacturer.
A only
Identify the sampling designs that use voluntary response sampling. Check all that apply.
A pharmaceutical company advertises for subjects to participate in an online survey about insulin pumps for diabetics. An online poll is created for sports fans to vote on the winner for the Super Bowl. After each customer service call, callers are asked to stay on the line to complete a brief satisfaction survey.
To determine if carrot juice helps improve heart conditions, a juicing company asks a random sample of 100 adults about whether or not they drink carrot juice and their heart condition. The company finds an association between drinking carrot juice and healthy heart conditions. Which statement is true about a possible confounding variable?
A possible confounding variable is the amount of exercise. Those that drink carrot juice may be more concerned about their health and exercise more, which explains the healthy heart conditions.
Identify the sampling designs that use convenience sampling. Check all that apply.
A restaurant surveys all its breakfast customers about meal quality. A company that produces natural food flavorings conducts taste tests with all its employees. A veterinarian collects information from his or her clients about dog food brand preferences.
Which statement about stratified random sampling is true?
A stratified random sample is a combination of simple random samples selected from each of several strata.
A researcher needs to assign 10 subjects, numbered 0 to 9, to one of two treatment groups: A and B. Use the table of random digits, starting with the first row and first column, to carry out the random assignment. Select the correct random assignment using the table.
A: 0, 7, 5, 8, 1 B: 3, 4, 2, 6, 9
A runner would like to know what percentage of people clean up after their dog while walking on public trails. For the next week, he keeps track every time he observes a person cleaning up after their dog (or not) while he runs on the public trail. He found that four out of 20 dog owners do not clean up after their dog. Which of the following conclusions can we draw from this study?
A: We can infer that about 25% of all dog owners do not clean up after their dog while walking on the public trail. B: We can draw conclusions about cause and effect for the population of all people who walk their dog on the public trail. We can conclude neither A nor B
Which statement(s) are accurate about cluster sampling? Check all that apply.
It is convenient because groups of individuals located near each other are sampled. It is a more cost-effective and less time-consuming way of sampling. Forming representative clusters can be challenging.
Twenty people who claimed to have trouble sleeping volunteered to participate in a sleep study. Half of them were randomly assigned to take 10 mg of melatonin 20 minutes before bed and the other half were randomly assigned to listen to soothing music when they went to bed. The volunteers adhered to their treatments for two weeks. At the end of two weeks, the individuals who listened to soothing music reported a greater improvement to their sleep than those who took melatonin. Which of the following conclusions can we draw from this study? A: We can make inferences based on the results of this study to the population of all people who have trouble sleeping. B: We can draw conclusions about cause and effect for people like those who participated in the study.
B only
A tennis court official selects a random sample of 50 tennis balls that were slated for use in a highly contested match. He randomly assigns half of them to be subjected to 90 degree heat to replicate the presumed temperature at match time. The other half are run through a machine that replicates the action of hitting the ball 500 times. After the treatments, he inspects the balls for wear and tear. Which of the following conclusions can we draw from this study? A: We can make inferences based on the results of this study for the population of all tennis balls slated for use in the match. B: We can draw conclusions about cause and effect for the population of tennis balls slated for use in the match.
Both A and B
A sunscreen manufacturer tests a new water-resistant sunscreen by finding 120 volunteers at a community pool. The subjects are randomly assigned to one of two groups by drawing either a 1 or 2 marked on slips of equal-sized paper from a bag. Half of the subjects use an old formulation, and half use the new formulation over an 8-hour time frame on the same sunny day. Test administrators apply a measured amount of sunscreen to each subject at the beginning of the day and reapply it at regular intervals throughout the day. Test subjects are asked to remain in unshaded areas as much as possible during the test. The levels of sunburn are compared at the end of the day. Which of the following accurately describes the benefit, if any, of control in the experiment?
By controlling variables that may influence the response variable, we reduce variability in the response variable.
Residents were asked to identify the type of car they drive and the average miles per gallon (mpg) the car receives on the highway.
Complete the statements based on the information. The categorical variable is names of residents✔ types of carsnumbers of miles per gallon. The continuous quantitative variable is names of residentstypes of cars✔ numbers of miles per gallon.
A participant in an experiment who incorrectly believes she is receiving treatment and reports an improvement in their condition is experiencing
placebo effect
Does listening to music while running help runners run faster? Here are two designs involving a group of 20 competitive runners. I. Pair the runners by speed. Flip a coin to assign one runner in each pair to run a 5K while listening to music. The other runner does not listen to music. Compare difference (no music - music) in 5K times. II. Flip a coin for each runner. Let heads = run the 5K while listening to music. After the runner finishes, we record their time and they run the 5K again under the other treatment. Which matched pairs design is appropriate, if any? Why?
Design I is appropriate because the second design would confound fatigue with the effect of music.
A company that provides a free online language course wants to determine if learners would be willing to pay $12 per month for a premium version of the course. Which questions might lead to question wording bias? Check all that apply.
Do you think $12 is too much to pay for a premium version of the course? Would you pay $12 for a premium version of the course, given that learning a language has been shown to improve concentration skills and memory? Would you pay $12 for a premium version of the course even though it is currently free?
An employer wants to determine the amount of job satisfaction experienced by his employees. Which sampling method is most likely to result in undercoverage?
Employees are assigned to one of four pay scales. Randomly select a pay scale and survey every employee in that pay scale.
The manager of a movie theater is standing outside the theater complex one evening. He will be asking the moviegoers questions.
How much did you spend at the movies today?
A beauty product company conducts a study to test the effectiveness of a new shampoo to control split ends. One hundred subjects have volunteered to take part in the study, and will be split into a treatment group and a placebo group. The study leader will assign the subjects to the groups randomly using slips of paper. Which reason identifies why randomization is important?
It is important that subject characteristics such as hair length, hair color, and gender are distributed equally among the treatment groups.
Tessa conducts an experiment and obtains results that are statistically significant. What is meant by "statistically significant"?
It means that the results that Tessa obtained are too unusual to be explained by chance alone.
The results of a study on state climate are shown below. What are the variables in the study? Check all that apply.
July Average High (°F) July Average Low (°F) Time Zone
A psychologist wants to create a simplified random sample of eight of his 920 subjects. He will use a random number table. Use this table of random digits. Begin with row 1, column 1 and use three-digit number pairs. Complete the statements outlining the steps that the psychologist should take
Label: Label the students from 0 to 8 1 to 8✔ 000 to 919000 to 920. Randomize: Skip numbers greater than 919 and ignore repeats. Stop after 1✔ 810 students are selected. Select: Select the individuals that correspond to the randomly selected numbers ✔ 002, 757, 117, 377, 648, 204, 527, 127X 002, 990, 757, 117, 377, 648, 204, 527299, 571, 377, 820, 271, 423, 265.
A music teacher wants to conduct a survey of practice time of her 30 students. He wants to select an SRS of six students using a random number table. Use this table of random digits. Begin with row 1, column 1 and use two-digit number pairs. Complete the statements outlining the steps that the music teacher should take.
Label: Label the students from 1 to 6 X 1 to 30 ✔ 00 to 2900 to 30. Randomize: Skip numbers greater than 06✔ 2930 and ignore repeats. Stop after six students are selected. Select: Select the individuals that correspond to the randomly selected numbers ✔ 07, 13, 28, 18, 25, 2307, 58, 13, 47, 28, 65X 00, 07, 05, 08, 01, 03.
Which is the best example of selecting a systematic random sample?
Members of a population are listed in order of birthday, and every 5th person is selected until a sample of 100 people is formed.
Which best describes the process of selecting a cluster sample?
Members of a population are organized in clusters, each of which is representative of the population, and then whole clusters are randomly selected to make up the sample.
A sunscreen manufacturer tests a new water-resistant sunscreen by finding 120 volunteers at a community pool. The subjects are randomly assigned to one of two groups by drawing either a 1 or 2 marked on slips of equal-sized paper from a bag. Half of the subjects use an old formulation, and half use the new formulation over an 8-hour time frame on the same sunny day. Test administrators apply a measured amount of sunscreen to each subject at the beginning of the day and reapply it at regular intervals throughout the day. Test subjects are asked to remain in unshaded areas as much as possible during the test. The levels of sunburn are compared at the end of the day. Which of the following represent controls in the experiment? Check all that apply.
Number of hours of sun exposure Amount of sunscreen applied Intervals of sunscreen application
A college professor conducts an experiment to determine if students perform better on exams when they study alone or in small groups. A total of 150 students taking an introduction to sociology course volunteer to participate in the study. Students are randomly assigned either to study alone for an upcoming exam or are assigned to a study group. The exam grades are then compared. Which of the following accurately describes the benefit of random assignment in the experiment?
Students of different abilities are more likely to be evenly distributed, so any differences observed in the exam grades are more likely to be a result of the treatment.
A trucking company wants to evaluate whether a decrease in the weight of their trucks helps to increase gas mileage. The company randomly selects 100 of their truck drivers, driving trucks that are identical in every way other than weight, to monitor gas mileage over a 1-year period. Results showed an association between truck weight and gas mileage. Which is a possible confounding variable for the provided scenario?
The aggressiveness of the driver's driving style
In an activity, students are pulling marbles from a large jar containing blue and red marbles. In their sample, students will calculate the proportion of red marbles. Which of the following is a correct statement about sampling variability?
The larger the sample size of marbles, the closer the sample proportion of red marbles will be to the true proportion of red marbles in the jar.
A new cream was developed to reduce the irritation caused by poison ivy. To test the effectiveness, researchers placed an ad online asking for volunteers to participate in the study. One hundred subjects replied and were informed that one group would receive the new cream and the other group would receive a cream with no active ingredient. All 100 subjects were exposed to poison ivy. Fifty were then randomly assigned to the group with the new cream, and 50 were randomly assigned to the group with the cream with no active ingredient. After three days, the subjects' level of irritation was measured. Which of the following accurately describes the benefit of comparison in the experiment?
The level of irritation for both groups can be compared to see if the new cream had a significant effect.
A university wants to survey students to gather opinions regarding a tuition increase for their online degree programs. A sample is collected by stationing employees at high traffic areas near the student center to administer the survey to passing students. Select the statement that best describes the result of the nonresponse bias.
The nonresponse bias will likely underestimate the approval percentage for the online tuition increase for the population.
A news broadcast invites residents of a community to visit their website and vote for or against new legislation that will decrease benefits for the elderly.
The sampling method used by the news show is a convenience ✔ voluntary response sample. In this scenario, the effected demographic of elderly residents are equally ✔ lessX more likely to use technology to vote. As a result, the proportion of people who support decreased benefits will be correctly estimated ✔ overestimatedunderestimated for all residents of the community.
A school district sends an online survey to all parents of students in the district asking for feedback on proposed educational changes based on recent tax cuts.
The sampling method used by the school district is a convenience ✔ voluntary response sample. In this scenario, parents who feel strongly about the tax cuts are equally less ✔ more likely to respond. As a result, the negative feedback might be correctly estimated ✔ overestimatedunderestimated for all residents of the community.
The top vote-getters for the formation of a jazz ensemble are shown. Which column shows the individuals in the study?
student
The manufacturer of an anti-nausea medication is testing a new chewable product against its existing non-chewable version. The 90 participants are assigned numbers from 01 to 90, and a table of random digits is used to select the 45 participants who receive the chewable version. The design web illustrates the experiment. Complete the statement below to describe how the experiment would benefit from blinding.
The ✔ test subject should not be informed about the different versions of the medication to reduce the influence of administrator bias✔ the placebo effect
A bakery is experimenting with a new preservative for its bread recipes to determine how it affects shelf life. For 150 loaves to be baked, they assign the numbers 001-150 and use a random number generator to select 50 loaves to be baked using three different amounts of the preservative.
There are 0.5✔ experimental units in each treatment group. There are ✔ 150 experimental units in all. The large number of loaves baked for each group ✔ will allow for good comparison of the differences in shelf life.
An insurance company is interested in comparing three options for anterior cruciate ligament (ACL) reconstruction to see if one option is better than the others. The participants are 60 people with an ACL tear. They are randomly divided into six groups. Each group receives one of the three options for ACL reconstruction (so that each treatment is given to two groups total). The functionality in leg motion of these 60 people is recorded and compared 12 weeks after surgery. Complete the sentences to accurately describe the situation.
There are ✔ three treatments, and they are the insurance company✔ options for ACL reconstruction in the study. The experimental units are the three options for ACL reconstruction✔ 60 people in the study study duration of 12 weeks. Since the experimental units ✔ are human beings, they are called ✔ subjects
A nutritionist would like to estimate the number of times adults exercise each week. To collect information, the nutritionist emails the members of the local fitness center. Which of the following describes the bias that may arise from the results?
This is a voluntary response sample and likely overestimates the frequency of exercise.
In a study of more than 3,200 divorced couples, researchers from a therapist's office found that those couples where both partners had divorced parents were more than three times as likely to divorce than couples where both partners did not have divorced parents. Does this scenario describe a retrospective or prospective observational study?
This scenario describes a ✔ retrospective observational study.
A community is considering raising funds to pay for improvements to the community swimming pool. To measure the level of interest, community leaders went door-to-door in a few neighborhoods and interviewed residents. Of the 230 residents contacted, 157 support raising funds to pay for improvements. Which of the following represents the sample in this setting?
the 230 residents who were interviewed
An observational study of suburban towns reveals that towns with more dedicated park land tend to have higher median home prices. A real estate agent suggests that a town's crime rate is a more accurate predictor of median home price. What is the confounding variable in this study?
the crime rate
An environmentalist would like to compare the mean number of miles per gallon (mpg) obtained by filling up with E85 versus regular unleaded gasoline. To do so, he selects a random sample of 100 vehicle owners and asks them to report their fuel economy (in mpg) for their next fill-up. He notices that some of the participants drive compact cars, some drive mid-sized cars, some drive trucks, and some drive SUVs. The researcher wants to use a matched pairs design. In order to isolate the effect of fuel type on fuel economy, what should the researcher use as pairs?
vehicles of similar sizes
Is the sample mean time until blinking (x̄ = 36 seconds) statistically significant evidence that the true mean time that students can go without blinking is greater than 30 seconds? Use the results to answer the question.
yes In this case, 13 percent✔of the simulated sample means are ✔ 36 or more, which is less than 5 percent
Identify the sampling designs that use convenience sampling. Check all that apply.
A grocery chain uses information from customer purchases to select products for future promotions. The first three people arriving at a movie theater are asked about their favorite movie genre. The drama club interviews patrons of the play about their interests in fine arts.
A restaurant wants to determine how much their customers like the dinner specials prepared by the new restaurant chef. Which survey method is most likely to lead to response bias?
Create a survey that is administered by the waitstaff prior to the customer leaving the restaurant.
Researchers conducted a study on the effects of exercise on mood. To form the sample, researchers went to a public mall and randomly selected a person who walked by to survey, and then they surveyed every 5th person after that until they had a sample of 30 people.
For the sampling procedure in this study, the researchers used cluster sampling X stratified random sampling ✔ systematic random sampling.
Researchers conducted a study on the effects of recess on elementary-student learning. To form the sample, researchers randomly selected elementary schools from across the country and included all students at each selected school.
For the sampling procedure in this study, the researchers used ✔ cluster sampling
A professor wants to create an SRS of 15 out of his 185 students. He labels his subjects as follows: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, . . . 185 Which statements accurately describe his labels? Check all that apply.
He did not label properly; he should have stopped at label 184. He did not label properly; the labels do not contain the same number of digits.
A hospital employs 60 nurses. The hospital human resources director wants to understand what incentives motivate nurses to work various shifts. A random sample of 25 nurses was selected to receive an anonymous survey. Of those selected, 19 completed the survey.
In this scenario, the population is 19 nurses X 25 nurses ✔ 60 nursesall hospital employees. In this scenario, the sample is ✔ 19 nurses25 nurses 60 nurses all hospital employees.
A biologist is studying the migratory patterns of sandhill cranes. His study focuses only on sandhill cranes that are bred and hatched in Alaska, and eventually migrate south to warmer climates. Each year he randomly tags a sample of 50 cranes with GPS trackers to gather data about their migratory patterns.
In this scenario, the population is all sandhill cranes ✔ Alaskan-bred sandhill cranes50 tagged cranes. In this scenario, the sample is all sandhill cranes Alaskan-bred sandhill cranes ✔ 50 tagged cranes.
A software company conducted a study about stress in the workplace for IT administrators. Which questions result in data that is categorical? Check all that appl
Is your job as an IT administrator stressful? What is your biggest source of stress? How has your job impacted your personal life? Have you ever considered switching careers because of on-the-job stress?
Which statement(s) apply to stratified random sampling? Check all that apply.
It can provide better estimates than a simple random sample. The researcher needs some knowledge of the population in terms of characteristics relevant to the study. Creating strata of similar individuals to sample from reduces variability. It can be difficult to obtain with a very large population.
A biologist wants to create an SRS to study the effect of a medication on the respiration rate of his subjects. He places the ID number of each of the subjects into a box, shakes the box, and chooses 10 of the ID numbers without looking. Which statement best describes this sample?
It is both a random sample and an SRS.
An article in a psychology journal claims that young students who play a musical instrument tend to have higher test scores on state math exams. To assess the claim, a government official considers two methods to collect data. Method 1: Contact many city schools and ask them to provide summary data on state math exam performance and students who participate in music lessons. Method 2: Choose two city schools and provide free music lessons to students who register. At the end of the year, compare state math exam scores for students who participated in the music lessons with the scores for those who did not. Which method describes an observational study?
Method 1 is an observational study because past data are collected and analyzed.
Researchers conducted a study on the effects of practice time of athletes on their endurance. To form the sample, researchers grouped the population by sport and then randomly selected 25 athletes from each group. Which statement identifies the sampling procedure used and gives a valid reason?
Stratified random sampling: subjects were randomly selected from each sport.
In an experiment to test the effectiveness of an energy supplement, participants are randomly assigned to groups by using a table of random digits. Which of the following best describes the control group in the experiment?
The control group is the group who received protein bars without the energy supplement.
A doctor wants to determine if a new medication for cholesterol is more effective than the previous medication. The doctor asks her patients if they would like to take part in a study for a new medication, and 30 patients currently taking medication for cholesterol volunteer to participate. Which of the following would be an appropriate procedure for this experiment?
The doctor needs to randomly assign 15 patients to the new medication and 15 to the original medication to even out the variability between the patients.
In an experiment to test the effectiveness of an energy supplement, participants are randomly assigned to groups by using a table of random digits. Which of the following accurately describes the benefit of comparison in the experiment shown in the design web?
The energy levels of those in the treatment group and in the control group can be compared to determine if the ingredient had a significant effect.
A speed training service wants to explore the effectiveness of some of the classes offered to their clients. They randomly select 300 high school athletes and record their 50-meter dash time. The 300 high school athletes are then randomly assigned to three groups with 100 in each. One hundred athletes will take a circuit training class, 100 athletes will take an interval training class, and 100 athletes will take a plyometrics training class. At the end of 10 weeks of taking these classes, their 50-meter dash time will be recorded a second time. Their times will be analyzed to see which class showed the greatest overall improvement in times. Select all the sentences that correctly identify the components of the experiment.
The experimental units are subjects. There are three treatments. One treatment is a circuit training class. The factor is the type of class.
A pharmaceutical company is interested in comparing four brands of sleep medication to see which brand is best at relieving sleep pattern symptoms, primarily insomnia. The participants are 80 people with sleep pattern symptoms. They are randomly assigned to four groups of 20 participants. Each group receives one of the four brands of sleep medication. The improvement in the sleep pattern of the 80 participants is recorded 6 weeks after taking the medication and the average improvement is compared among the four treatment groups. What are the factor(s) and level(s) of this scenario?
The factor is the ✔ sleep medication The levels are the 6 weeks of the experiment✔ 4 different treatments, or medications
A study is being conducted on the number of people who frequent a certain breakfast buffet and how often they visit the buffet during a six-month period. Complete the statements based on the information.
The individuals in the study are the location of the breakfast buffet ✔ people who visit the breakfast buffetnames of the six months in the study. The variable in the study is the ✔ number of times a person visits the buffet in six monthsduration of time a person stays at the buffet cost of the buffet.
A company that manufactures car seats completes quality control tests per government regulations. The quality control department randomly selects 20% of the seats manufactured to evaluate safety conditions. Of those seats, 0.0005% indicated a safety problem. Which of the following describes the population and sample?
The population is 100% of the car seats and the sample is 20% of the car seats.
A researcher at Ohio State University is growing bacteria in her laboratory for a study. She extracts a group of 50 cells to observe under a microscope for cell structure. Which of the following describes the population and sample?
The population is all growing bacteria in the lab, and the sample is the group of 50 extracted cells.
Which statement(s) give advantages or disadvantages of systematic random sampling? Check all that apply.
The population size does not need to be known. Unknown patterns of differences in the population can be difficult to detect. Every member of a population does not need to be known.
A company that provides a free online language course wants to determine if learners would be willing to pay $12 per month for a premium version of the course. They ask the question, "Do you think $12 is too much too pay for a premium version of the course?" Select the statement that best describes the probable result of the question wording bias.
The question wording bias will likely underestimate the number of people willing to pay $12 per month for a premium version of the course.
Which of the following statements are always true about matched pairs experimental designs? Check all three that apply.
The randomization is carried out separately within each pair. Matched pairs design is a form of blocking, with each block containing two experimental units. The randomization within a matched pairs design can be accomplished with a coin toss.
A restaurant wants to determine how much their customers like the dinner specials prepared by the new restaurant chef. A survey is administered by the waitstaff prior to the customer leaving the restaurant. Select the statement that best describes the probable result of the response bias.
The response bias will likely overestimate the likeability of the chef-prepared dinner specials.
A botanist wants to create an SRS of size 10 from 60 plants that are arranged in an array of 10 rows of 6 plants each. She numbers the plants in each row from one to six. For each of the 10 rows, she rolls a six-sided number cube and selects the plant corresponding to the number rolled. Which statements are true? Check all that apply.
The sample is a random sample. Each plant has an equal chance of being selected.
The manager of a machine shop wants to create an SRS of 20 parts to check for defects in the parts coming off an assembly line. She selects every other part that comes off the line until she has selected a total of 20 parts. Which statements are true? Check all that apply.
The sample is not a random sample. There are restrictions placed on the sample.
A researcher wants to create an SRS of seven out of 85 subjects. She labels her subjects and then selects seven numbers by moving from left to right, across row 1 of the table. Use this table of random digits. Begin with row 1, column 1 and use two-digit number pairs. Her list of seven numbers is 69, 17, 80, 45, 21, 17, and 37. Which statement accurately describes the list of seven numbers?
The seven numbers were not chosen properly because the list includes repeats.
A study is testing the effectiveness of a new headache medication. Sixty people who regularly suffer from headaches are assigned numbers from 01 to 60, and a table of random digits is used to select 30 subjects. The 30 selected subjects are given the medication, and the remaining 30 subjects are given placebo pills to take when they get a headache. The subjects who received the medication reported a strong improvement in symptoms, and the subjects who received the placebo reported a moderate improvement in symptoms. The subjects in the ✔ control groupX treatment group who received the X medication✔ placebo pill reported no improvementminimal improvement✔ moderate improvementX strong improvement in their headache symptoms during the experiment. This is a possible placebo effect.
The subjects in the ✔ control group ✔ placebo pill ✔ moderate improvement in their headache symptoms during the experiment. This is a possible placebo effect.
A teacher wants to quantify how doing homework affects test scores. She has 60 statistics students. For the upcoming chapter she decides to randomly assign some students a daily homework assignment, which they will have to turn in for scoring. The other students will be told that they have no homework. Some of her students are advanced and others are on-level. She wants to conduct a randomized block design for this experiment. Which statements are true? Check all that apply.
The teacher should block by student ability level—advanced or on-level. The students should be given homework, or not be given homework, separately within each block. The size of each block depends on the number of advanced and on-level students.
A physician is testing the effectiveness of two new exercise plans on 70 subjects. To assign the subjects to the two treatment groups, he writes "Plan 1" on one slip of paper and "Plan 2" on another slip of paper. He randomly picks one of the slips, and assigns the first 35 subjects who signed up to that plan, and assigns the last 35 subjects to the other plan. Select the statement that best describes the composition of the treatment groups.
The treatment groups might not be comparable, because the first 35 subjects to sign up for the study might share a characteristic related to exercise, such as high motivation.
A telemarketing company is conducting a study of new calling scripts. A group of 75 employees will be randomly assigned to three new scripts. The study designer numbers the subjects from 01 to 75, and uses a table of random digits to select 50 unique, two-digit numbers in the range 01-75. The 25 subjects corresponding to the first 25 random two-digit numbers will be assigned to script 1, the second 25 to script 2, and the 25 remaining subjects to script 3. Select the statement that best describes the composition of the treatment groups.
The treatment groups should be comparable, because characteristics of the subjects should be roughly equivalent among the three groups.
An employer wants to determine the amount of job satisfaction experienced by his employees. Employees are assigned to one of four pay scales. Each employee from the top two pay scales are chosen for the sample. Select the statement that best describes the result of the undercoverage bias.
The undercoverage bias will likely overestimate the inferred job satisfaction for the population.
A veterinarian selected a random sample of 10 dogs to study their sleep patterns. Five of the dogs were randomly assigned to eat dry dog food and the other five dogs were randomly assigned to eat wet dog food. The data showed that dogs who ate wet dog food were more likely to sleep regularly than those who ate dry dog food. Does this scenario describe an observational study or an experiment?
This scenario describes an ✔ experiment.
A researcher wants to generate an SRS to study the blood pressures of a population of 100 athletes on four high school athletic teams. Use the drop-down menus to complete each statement.
To be considered an SRS, the athletes in the sample of size n must have the same chance of being selected from the population as X a group of n athletes from each team✔ every other group of athletes of size nX a group of size n with different blood pressures. To be considered an SRS, the sample ✔ cannot be biasedcan be biased may or may not be biased.
A therapist wants to study the effects of yoga and meditation on stress relief. She has 60 volunteers who experience varying levels of stress. Half of the participants will be assigned to practice yoga for one month and the other half will practice meditation. Before the experiment begins, all of the participants will be asked to rate their stress levels on a scale from 0 to 10, with 0 representing "no stress" and 10 representing "highest level of stress." At the end of one month, the participants will be asked to rate their stress levels again. The differences in stress levels will be compared. Which of the following describes a matched pairs design?
Volunteers are put together in groups of two based on stress level. For each group of two, a coin is flipped. If it lands on heads, then the first person is placed in the yoga group and if it is tails, then the first person is placed in the meditation group. The other person will be placed in the other group. After one month, the stress levels between the two participants are measured and compared.
A beauty product company conducts a study to test the effectiveness of a new shampoo to control split ends. One hundred subjects have volunteered to take part in the study and will be divided into a treatment group and a placebo group. The study leader will assign the subjects to the groups randomly using slips of paper. Select each statement that could describe an appropriate step in the labeling process.
Write "treatment group" on 50 slips of paper and write "placebo group" on 50 slips of paper. Number the subjects from 1 to 100, and write the numbers 1 to 100 on the slips of paper. Write the name of each subject on a slip of paper.
A concerned mother wants to ensure that her children are drinking pure water. Specifically, she wants to compare the water quality that comes from her kitchen sink to that which runs through her stand-alone water-filtration system. She purchases a device that measures the contamination of the water on a scale of 0-100, where 0 indicates no contaminants and 100 means the water is fully contaminated and unsuitable for human consumption. She selects 30 samples of water from her kitchen sink. She randomly selects 15 of the samples to run through the water-filtration system. Afterward, she measures the contamination of all 30 samples of water, cleaning the device between each measurement. She computes the average contamination score for the 15 samples of water that came directly from her sink, as well as the average contamination score for the 15 samples of water that came through the filtration system. Is this a completely randomized design? Explain.
Yes, she assigned the samples of water to the treatments completely at random.
In a large ball pit, 20% of the balls are red. You plan to jump in and randomly select 10 balls. Which statement is true?
You will likely have one to three red balls in your sample.
A student would like to estimate the average number of text messages sent by cell-phone users in a day. Which of the following methods would provide a voluntary response sample?
a text poll provided during a nightly news broadcast
A survey about rideshare services includes the following questions: Which rideshare services have you used in the past two months? Which rideshare service is your favorite? What is your age? How many miles did you travel? Which are the variables in the study? Check all that apply.
age favorite rideshare service miles traveled by rideshare service types of rideshare services
Researchers would like to assess the overall health of white pine trees in a state park. Using a computer program, the researchers selected 100 random points in the state park and assessed the trees closest to the selected points. Of the 100 trees selected, 24 showed damage to their lower limbs. Which of the following describes the population in this setting?
all white pine trees in the state park
Data from a study on state populations are being gathered. The data set contains information about the state name, the state bird, the population in 2018, the percent of population increase or decrease since 2010, and the area (in square feet) of the state. Which variable would be classified as categorical?
state bird
Over morning announcements, the principal states that only 20% of the senior class turned in their graduation survey. You find the principal's statement hard to believe because the office previously announced that a coupon for a free large pizza would be given to seniors who turn in their graduation survey. At lunch time, you select a random sample of 10 seniors and ask them if they turned in their graduation survey. Six seniors say "yes." Using technology, the student simulated the sample percent of seniors that turned in their survey using 50 random samples of 10 students under the assumption that 20% of all seniors turned in their survey. Here are the results. Is the sample percentage obtained by the student (60%) statistically significant evidence that greater than 20% of seniors turned in their graduation survey?
✔ Yes. In this case, ✔ 0 percent of the simulated sample means are ✔ 60 percent or more, which is ✔ less than 5 percent.
