KHAN ACADEMY
Mr. Thompson runs his own printing and bookbinding business. He suspects that the machine isn't putting enough glue into the book spines and decides to inspect his most recent order of 70 textbooks to test his theory. He numbers them 01-70 and, using the random digit table printed below, selects a simple random sample of 5 books to check. Which books are in the sample? 05007 16605 81194 14873 04197
05,66,19,41,48
Mr. Thompson runs his own printing and bookbinding business. He suspects that the machine isn't putting enough glue into the book spines and decides to inspect his most recent order of 70 textbooks to test his theory. He numbers them 01-70 and, using the random digit table printed below, selects a simple random sample of 5 books to check. Which books are in the sample? 85063 55810 10470 08029 30025
06, 35, 58, 10, 47
There are 90 students in a lunch period, and 5 of them will be selected at random for cleaning duty every week. Each student receives a number 01-90 and the school uses a random digit table to select a simple random sample of 5 students. Which 5 students should be assigned cleaning duty? 06915 72954 10167 12142 26492
06,57,29,54,10
Willy runs a small company with 10 employees. He decides to pick a simple random sample of3 employees to go on a business trip. He numbers them 0-9 and uses the random digit table printed below to select the sample. Which employees are in the sample? 10056 42211 65491
1,0,5
Mia is considering moving to a different apartment complex than where she currently lives. To better understand rent prices, she takes a large random sample of apartment complexes in her city and finds out the monthly cost of rent for a 1-bedroom apartment at those complexes. She finds the average rent of apartments in the sample is about $800 per month. Mia can safely generalize this result to which population?
All 1-bedroom apartments in her city only *Since the sample of 1-bedroom prices was randomly selected from all complexes in her city, the results can safely be generalized to this population.
A large random sample of first-year students at Duke University—a private university in North Carolina—was polled about their overall satisfaction with campus living. To which population can the results of the poll safely be generalized?
All first-year students at Duke University only *Since the sample was randomly selected from first-year students at Duke University, the results can safely be generalized to this population.
First-year students at a certain large university are required to live on campus in 1 of the 24 available residence halls. After their first year, students have the option to live away from campus, but many choose to continue living in the residence halls. Estella oversees 12 of these residence halls. Her department surveyed a large simple random sample of first-year students who live in those 12 residence halls about their overall satisfaction with campus living. Estella can safely generalize the results of the survey to which population?
All first-year students, but only those who live in these 12 residence halls *Since the sample was randomly selected from first-year students who live in those residence halls, the results can safely be generalized to this population.
At Amira's pizza shop, they open a fresh batch of pizza sauce for every 10th pizza they make. Amira decides she wants to take a sample of pizzas in a given day and evaluate their overall quality. Her shop makes approximately 150 pizzas per day, and she doesn't want to sample more than 10 pizzas for time's sake. Amira decides to use a systematic random sample where she'll evaluate every kth pizza made that day. Why might Amira choose k=17 instead of k=10?
Amira will sample more than 10 pizzas if she uses k=10. *She doesn't want to sample more than 101010 pizzas, and 150/10= 15. In terms of pizza sauce freshness, Amira will likely get a more representative sample if she uses k=17.
A study published in the journal Environmental Health found that flight attendants get cancer more often than the general population. The 5,366 flight attendants in the study had higher incidence rates for every type of cancer examined, even though they had relatively lower rates of smoking and obesity. What type of study is this, and what is the response variable?
An observational study where the incidence rate of cancer is the response variable *The people in this study weren't assigned to a treatment, so this study is observational. Since they are using type of person (flight attendant or not) to explain the incidence rate of cancer, the incidence rate of cancer is the response variable
Employees at a video streaming website suspect that users on desktop computers spend more time on their website than users on mobile devices. They plan on taking a large random sample of users to see if their suspicions are correct. What type of study is this, and what is the explanatory variable?
An observational study where type of device is the explanatory variable *The users aren't being assigned to a treatment, so this study is observational. Since they are using type of device to explain the time spent on the website, type of device is the explanatory variable.
An insurance company wants to study whether offering incentives for preventative care reduces overall health care costs. They select a random sample of 200 of their customers. They use a random number generator to select 100 customer account numbers to offer the incentive. The remaining 100 customers are assigned to the control group. What type of experiment design is this?
Completely randomized
An online retailer wants to study whether more lenient return policies increase purchasing behaviors. They select a random sample of 2000 customers who have made purchases in the past year. They use a random number generator to select 1000 customer account numbers to assign to the treatment group. The remaining 1000 customers are assigned to the control group. What type of experiment design is this?
Completely randomized
A company wants to study the effectiveness of a new pain relief medicine. They recruit 100 volunteers who suffer chronic pain. They assign each subject a number from 1 to 100 and use a random number generator to assign the first 50 subjects selected to the treatment group. The remaining 50 subjects are assigned to the control group. What type of experiment design is this?
Completely randomized *This study is an example of a completely randomized design since each subject is randomly assigned to one of the treatment groups without extra consideration to other variables.
A researcher polls people as they walk by on the street. What type of sample is this?
Convenience sample
A quality control engineer is curious about the thickness of paint on a car at her factory. She randomly selects 30 points on the car and measures the paint thickness at each of those points. Identify the population and sample in this setting.
The population is every possible point on the car; the sample is the 30 selected points.
Forest rangers at a national park want to take a sample of trees to estimate what proportion of trees in the park are infected with a certain disease. The population of trees in question is divided by a creek. East of the creek, most of the trees are oak. West of the creek, most trees are cedar, which are more likely to be infected. The rangers are considering taking a stratified random sample using each side of the creek as strata. They'll sample trees from each side proportionately based on the total number of trees on each side. Why might the rangers choose stratification instead of a simple random sample to estimate the proportion of infected trees?
In repeated sampling, estimates from this sort of stratified sample would likely vary less than estimates from simple random samples. A stratified random sample reduces the likelihood of getting disproportionate numbers of cedar or oak trees in the sample.
An insurance company wants to study whether offering incentives for preventative care reduces overall health care costs. They select a random sample of 200 of their customers. The company ranks the customers according to total health care costs for the previous year. For every 2 customers, in order, from the list, the insurance company randomly assigns one customer to be offered the incentive and the other to the control group. What type of experiment design is this?
Matched pairs *The subjects were first put into pairs with another similar customer, and it was randomly determined which member of each pair was offered the incentive and which one wasn't, so this study used a matched pairs design.
An online retailer wants to study whether more lenient return policies increase purchasing behaviors. They select a random sample of 2000 customers who have made purchases in the past year. The company ranks the customers according to total cost of purchases made the previous year. For every 2 customers, in order, from the list, the online retailer randomly assigns one customer to the treatment group and the other to the control group. What type of experiment design is this?
Matched pairs *The subjects were first put into pairs with another similar customer, and it was randomly determined which member of each pair would receive the treatment and which would receive the control, so this study used a matched pairs design.
A politician asks his neighbors their opinions about a controversial issue. What type of sample is this?
None of the above (convenience)
A popular online video game can be played on multiple platforms: video game consoles, personal computers, and mobile devices. The game offers 3 gameplay modes: solo, duo, and squad. Lee and Avery regularly play matches as teammates in duo mode on a video game console. They are curious how their average scores per match compare to other players. They use the game's website to take a large random sample of duo mode players on any platform. The sample has a mean of 585 points per match. For which population is 585 points a legitimate estimate of the average points per match?
Only duo mode players who play on any platform *Since the sample was randomly selected from duo mode players on any platform, the results can safely be generalized to this population.
A famous study examined the smoking habits of British doctors and whether or not the doctors developed various types of cancers. Participants responded to questionnaires about their smoking habits and health in 1951, 1957, 1966, and many more times all the way up to 2001. What type of observational study is this?
Prospective Study
Lilian's favorite magazine published 50 issues last year, and each issue contained approximately 250 pages. She wants to take a cluster random sample of about 1000 total pages to estimate what proportion of all pages contained an advertisement. Which of these strategies will accomplish her intended design?
Randomly select 4 issues, and examine every page in those issues.
A concert venue offers tickets in 3 zones: orchestra, grand tier, and balcony. Tickets in the orchestra zone are most expensive, and tickets in the balcony zone are least expensive. Managers of the venue want to survey approximately 150 guests at an upcoming concert about their overall experience. They want to take a stratified random sample of guests based on the venue's zones. Which of these strategies will accomplish their intended design?
Randomly select 50 tickets from each zone and invite those guests to participate in the survey. *This is a stratified random sample since it involves selecting some members from all of the groups (zones).
A college professor wants to survey a sample of students taking his course. Here are some details about his course: -He teaches 5 sections of the course. -There are 250 total students across those sections. -There are 50 graduate students and 200200200 undergraduate students taking the course. -Each section has about 50 students (some graduate and some undergraduate). The professor wants to take a sample of 30 students for a survey. He suspects that opinions on the survey may differ the most based on student type (graduate or undergraduate), so he wants to design his sample to take that into account. Which of these strategies will accomplish his intended design?
Randomly select 6 graduate students and 24 undergraduate students for the survey. *A stratified sample like this guarantees that each type of student is proportionately represented in the survey.
An airline wants to survey customers about their overall satisfaction. They take a random sample of 1,000 customers who have flown in the past month and email them a survey. The email also offers those who complete the survey a $25 gift card that can be used almost anywhere. Which of these is the best example of nonresponse bias?
Satisfied customers might be less likely to complete the survey than dissatisfied customers. *This would be nonresponse, which is when people of interest can't be reached or refuse to participate. If satisfied customers opt out, then the survey results might suggest that customers are less satisfied overall than they really are.
A teacher puts students' names in a hat and chooses without looking to get a sample of 3 students. What type of sample is this?
Simple random sample
A tutoring company has offices where students physically attend a test prep course. The company recently created an online test prep course, and they wonder if it produces similar or different outcomes than their in-person course. They recruit 50 students who are willing to try the online course. On average, those 50 students produced significantly better outcomes than students historically do in the in-person course. The company concludes that the online course produced better outcomes than the in-person course for these students. Which of these concerns makes their conclusion inappropriate?
Some of the 50 students should have been assigned to a control group that used in the in-person course.
A dentist wants to conduct a survey via telephone to determine what percent of all adults in their city floss daily. Which of these is the best example of response bias?
Some people might feel pressured to say they floss daily even though they don't.
A large company surveys 100 employees by taking random samples of 10 managers and 90 non-managerial employees. What type of sample is this?
Stratified random sample
A truck manufacturer selects 3 trucks at random from each of 6 models for safety testing. What type of sample is this?
Stratified random sample
A majority of people who receive surveys in the mail don't respond. Researchers were curious which type of reward would be most effective: send someone $10 after they mail a completed survey back, or, send someone $5 with a survey as an advanced "thank you" that they can keep whether or not they participate. The researchers chose a random sample of 1200 adults and randomly assigned each of them to one of three groups: $10 after, $5 advance, or no reward at all. They found that people in the $5 group were significantly more likely to send the survey back than people in either of the other groups. What conclusion can they draw from this study?
The $5 in advance caused the difference in survey completion.
Various types of doctors attended a large medical conference. Someone leading a session asked the 30 doctors in attendance how many years of experience they each had. The 15 dermatologists at the session had an average of 8 years of experience. For which population is 8 years a legitimate estimate of the average experience?
The dermatologists at that session only *The 15 dermatologists at this session weren't randomly selected from a larger population. They may not be representative of all doctors or even all dermatologists on the question of experience.
Researchers recruited participants for a wine tasting study that included a variety of wines in terms of style and price. The participants tasted a series of wines in a random order. Participants could look at the bottle for each wine so they could take its price and label information into account as they tasted and rated each wine. The participants rated the more expensive wines significantly better tasting than the less expensive wines. The researchers carrying out the study conclude that more expensive wines taste better. What is a confounding variable that makes their conclusion inappropriate?
The lack of blinding *Seeing the price of each wine is a confounding variable. The participants might already think that expensive wines will taste better than cheaper wines.
A group of librarians is interested in the numbers of books and other media that patrons check out from their library. They examine the checkout records of 150 randomly selected adult patrons.
The population is all adult patrons of the library; the sample is the 150 patrons selected.
A safety inspector conducts air quality tests on a randomly selected group of 7 classrooms at an elementary school. Identify the population and sample in this setting.
The population is all classrooms in the elementary school; the sample is the 7 classrooms selected.
A recent study showed that players of a certain video game tend to perform better if they take breaks. The study involved analyzing data from 242000 matches played by 16665 players of League of Legends, a popular online game. The data showed that players who took regular breaks, on average, performed better than those who did not. What conclusion can they draw from this study?
There was an association between taking breaks and better performance, but it's not necessarily a causal relationship.
Researchers working on a vaccine for HIV recruited over 16,000 volunteers for a study. Each volunteer was randomly assigned to receive monthly injections of either the vaccine or a placebo for a year. The researchers were curious if subjects who received the vaccine would be less likely to contract HIV than subjects who received the placebo. What is the main reason for randomly assigning the subjects?
To create groups that are as similar as possible so the main difference between the groups is the treatment *The goal of random assignment is to roughly balance other variables (age, gender, risk of HIV, and so on) between the treatment groups. This way, the main difference between the groups is the vaccine, so we can make comparisons.
Researchers recruited over 1000 patients with chronic back pain to participate in a study about the benefits of acupuncture. Each subject was randomly assigned to one of these treatment plans: traditional Chinese acupuncture, placebo acupuncture, and conventional pain treatment (medication and physical therapy).
To create groups that are as similar as possible so the main difference between the groups is the treatments *The goal of random assignment is to roughly balance other variables (age, gender, pain level, attitudes, and so on) between the treatment groups. This way, the main difference between the groups is the explanatory variable, so we can make comparisons.
A psychologist thinks that meditation might be a useful tool for patients trying to lose weight. They design an experiment and recruit volunteers who are all interested in losing weight. Half of the subjects (determined at random) will attend weekly guided meditation sessions and receive access to a diet and exercise program. The other half of the subjects will just have access to the diet and exercise program. What is the primary purpose of including a group who doesn't attend meditation sessions?
To serve as a control group for comparison
Jillian has been updating the design of a media streaming website. She wonders if users will spend more time on the site with the new design, so she designs a study. She starts with a random sample of 1000 users and randomly assigns half of them to the old design and half of them to the new design. After a week, she notices that users with the new design spend significantly longer on the site than the users with the old design. Can we conclude that the new design caused users to spend more time on the site? Why?
Yes, because the users were randomly assigned to treatment and control groups
A company makes a bracelet containing magnets that they claim improves balance and overall athletic performance. Researchers recruit volunteers for an experiment. The subjects will test the effectiveness of the bracelet by performing a variety of athletic challenges with and without the bracelet. Each subject will do each challenge 333 times: wearing the actual bracelet, wearing a placebo bracelet, and wearing no bracelet at all. The order will be randomized for each activity, subjects won't know which bracelet is which. Why did the researchers include the scenario where subjects wear no bracelet at all?
To serve as a control group for comparison *Comparing the actual bracelet to the placebo bracelet is useful for seeing if the magnets improve performance. Including a group that doesn't wear a bracelet at all is useful for seeing if simply wearing a bracelet improves performance.
Sadie is redesigning her company's website. She wants to carry out an experiment that involves randomly assigning visitors to either the existing design or the new design. A user's experience is slightly different depending on what type of device (mobile or desktop) they use, so Sadie wants to use a randomized block design. How should Sadie form the blocks?
Users within each block should use the same type of device as each other. *Sadie should block users based on variables she knows might impact the results of the experiment—like what type of device the user has. Each type of device should be a block, so some subjects with each type of device will see the new design while others see the existing design.
Willy runs a small company with 10 employees. He decides to pick a simple random sample of 3 employees to go on a business trip. He numbers them 0-9 and uses the random digit table printed below to select the sample. Which employees are in the sample? 37374 75202 44753
3,7,4
There are 90 students in a lunch period, and 5 of them will be selected at random for cleaning duty every week. Each student receives a number 01-90 and the school uses a random digit table to select a simple random sample of 5 students. Which 5 students should be assigned cleaning duty? 96565 05007 16605 81194 14873
56,50,07,16,60
Willy runs a small company with 10 employees. He decides to pick a simple random sample of 3 employees to go on a business trip. He numbers them 0-9 and uses the random digit table printed below to select the sample. Which employees are in the sample? 69290 03600 05376
6,9,2
Estelle's cornfield is divided into 6 regions. She wants to know if a new pesticide is as effective as the pesticide that she currently uses. She randomly assigns each of the 6 regions to either the new or current pesticide for a month, and she'll compare the effectiveness of the pesticides. What type of experiment design is this?
A completely randomized design *The 6 regions were each randomly assigned to either the treatment (new pesticide) or control (current pesticide). They were not grouped in any way with random assignment happening within each group, so this is a completely randomized design.
Rita teaches environmental biology. She has 2 forms of a midterm exam, and she wonders if either form is harder than the other. She teaches approximately 200 total students in 4 sections of the class. She randomly assigns half of the students in each section to each form of the exam. Rita will then see if the average scores are significantly different between each form. What type of experiment design is this?
A randomized block design where the 4 sections are the blocks *In a randomized block design, random assignment is carried out within each block. The students were first divided by section, and random assignment occurred within each section, so the sections are the blocks.
A pharmaceutical company is carrying out a trial for a new flea prevention medication that is designed to work for dogs or cats. They recruit pet owners and ask them what flea prevention they currently use. They randomly assign half of the dogs in the study to the new flea prevention medication, and the other half of the dogs in the study will receive their current prevention. A similar process is carried out with the cats in the study. What type of experiment design is this?
A randomized block design where the pet types (dogs and cats) are the blocks *In a randomized block design, random assignment is carried out within each block. The pets were first divided by type, and random assignment occurred within each type, so the types are the blocks.
Grace was curious if married people were more likely to be safe drivers than unmarried people. Grace took a random sample of car accident records from the past 5 years in her country, and she calculated what percent of accidents in the sample were caused by married people. She compared that result with the percentage of all drivers in the country that were married during that time period.
A retrospective study
Annabella was curious about why people choose to skydive. She randomly selected 10 flights that were carrying skydivers and interviewed all of the skydivers on the flights about their motivations. What type of observational study is this?
A sample survey
The library where Kara works is planning to add a maker space where members can share equipment and services to create crafts. Kara randomly selected members from their database, then contacted them to ask what kinds of equipment and services they would be most likely to use. What type of observational study is this?
A sample survey
Vishal was interested in the relationship between a person's age and their musical preferences. He randomly selected numbers listed in his city's telephone directory and called those numbers. Whenever someone answered and agreed to be questioned, he asked them for their age and interviewed them about their musical preferences. What type of observational study is this?
A sample survey
An airline offers a certain flight once per day that usually contains about 250 passengers. The flight offers seats in first class (most expensive), business class, and economy class (least expensive). The airline wants to survey 500 passengers of this flight about their overall satisfaction. The passengers will be selected using a cluster random sample where each flight is a cluster. Why might the airline choose a cluster random sample instead of a simple random sample in this setting?
A simple random sample might result in a disproportionate number of passengers from one or more class, but a cluster sample is less likely to suffer this issue. Contacting all of the passengers on a few flights will probably be more efficient than contacting passengers spread out across many flights.
A concert venue offers tickets in 3 zones: orchestra, grand tier, and balcony. Tickets in the orchestra zone are most expensive, and tickets in the balcony zone are least expensive. Managers of the venue want to survey approximately 150 guests at the next concert about their opinions on the schedule of shows in the upcoming season. Why might the managers choose a systematic random sample instead of a simple random sample?
A systematic sample can save time by selecting guests as they enter rather than looking for guests selected in a simple random sample.
Ava is considering moving to a neighborhood in a different city and state than where she currently lives. To better understand home prices in that area, she looks up the values for a large random sample of homes in that city and calculates their average price. Ava can safely generalize this result to which population?
All homes in that city, but not the entire state *Since the sample was randomly selected from all homes in that city, the results can safely be generalized to this population.
A large random sample of adults aged 40 to 50 living in San Francisco, California, was polled about how likely they are to purchase an electric vehicle sometime in the next year. To which population can the results of the poll safely be generalized?
All people aged 40 to 50 living in San Francisco only *Since the sample was randomly selected from adults aged 40 to 50 living in San Francisco, the results can safely be generalized to this population.
An administrator at a large university is curious how students rate the quality of the athletic facilities at the university. They decide to survey a random sample of 80 students who participate in the university's intramural football league. The survey shows that 54% of those asked said they were "very satisfied" with the athletic facilities. For which population is 54% a legitimate estimate of the percent of students that are "very satisfied" with the athletic facilities?
All students at the university who participate in the intramural football league *Since the sample was randomly selected from students who participate in the university's intramural football league, the results can safely be generalized to this population.
According to a study published in the journal Psychological Medicine, ayahuasca—a drink made of Amazonian plants—can help people with depression. The study involved 29 participants who all had depression. Doctors gave each of the participants either ayahuasca or a placebo beverage that looked and tasted similar. Those who drank ayahuasca showed significantly lower levels of depression compared to those who drank the placebo beverage. What type of study is this, and what is the response variable?
An experiment where depression level is the response variable *The participants were assigned to a treatment, so this study is an experiment. Since the study used the type of drink to explain changes in depression level, depression level is the response variable.
A recent study showed that viral medications might be useful for fighting certain bacterial infections. Participants with gastrointestinal issues were assigned to either a placebo or viral medication for the first four weeks of the study, followed by an additional four weeks on the other treatment. Their symptoms showed significantly more improvement from the viral medication than the placebo. What type of study is this, and what is the explanatory variable?
An experiment where the type of treatment (viral or placebo) is the explanatory variable The participants were assigned to a treatment, so this study is an experiment. Since the study used the type of treatment to explain symptom improvement, the type of treatment is the explanatory variable.
According to a study published in the journal Social Psychological and Personality Science, people with religious affiliations live longer, on average, than those without religious affiliations. The study analyzed more than 1000 obituaries and accounted for other variables like sex and marital status. What type of study is this, and what is the explanatory variable?
An observational study where religious affiliation is the explanatory variable *The people in this study weren't randomly assigned to a treatment, so this study is observational. Since they are using religious affiliation to explain lifespan, religious affiliation is the explanatory variable.
A large gym with hundreds of members offers yoga classes. Members are free to take these classes at no charge, but not all members are interested, and some never take advantage of the yoga classes. Non-members can also take these classes, but they must pay a fee for each class. A manager at the gym is curious about overall satisfaction with these yoga classes, so they survey a large random sample of anyone who has taken a yoga class at the gym in the past year. They find that 78%, percent of those surveyed are "very satisfied" with the yoga classes. For which population is 78%, percent a legitimate estimate of the percent of people that are "very satisfied" with the yoga classes?
Anyone who has taken a yoga class at the gym in the past year, but not before that *Since the sample was randomly selected from anyone who had taken a yoga class at the gym in the past year, the results can safely be generalized to this population.
An experiment involving a new pain relief medication involves subjects being randomly assigned to one of two treatment groups. Subjects in one group will take a daily dose of the new medication, and subjects in the other group will take an existing common pain medication. All subjects will check in with a doctor every week to report their symptoms and any side-effects. What does it mean for this experiment to be double-blind?
Both the subjects and the doctors are unaware of who is taking which medication.
An airline company wants to survey its customers one day, so they randomly select 5 flights that day and survey every passenger on those flights. What type of sample is this?
Cluster random sample
Inspectors for a hospital chain with multiple locations randomly select some of their locations for a cleanliness check of their operating rooms. The inspectors check every operating room in the hospitals that were chosen. What type of sample is this?
Cluster random sample
A professor wants to study the effectiveness of a new study tool for a course. There are 150 students registered for the course. The professor assigns each student a number from 1 to 150 and uses a random number generator to assign the first 75 students selected to use the new study tool. The remaining 75 subjects are assigned to use the previous study tool. What type of experiment design is this?
Completely randomized *This study is an example of a completely randomized design since each subject is randomly assigned to one of the treatment groups without extra consideration to other variables.
A warehouse stores thousands of marble slabs of different shapes, sizes, and materials that are used for construction projects. The manager wants to estimate the average weight of these slabs. The slabs are arranged in stacks that have about 10 slabs of different varieties. The manager wants to weigh a random sample of 100 slabs. Why might the manager choose a cluster random sample instead of a stratified random sample in this setting?
Each stack has a variety of slabs, so choosing all of the slabs in some of the stacks should represent the population fairly well. *If each stack reflects the variety in the population, then choosing the stacks as clusters is a good way to get a sample that looks like the population. It will probably be easier to weigh heavy slabs that are stacked together rather than pulling out some slabs from different stacks. *By weighing entire stacks, the manager would only need to retrieve, weigh, and return about 101010 units. By weighing fewer slabs per stack, there are many more steps in the process and it is more complicated to track where to return the weighed slabs.
Valerie manages a team of 30 employees at a large company. She wants to survey members of her team on her performance as their manager. She holds an individual meeting with each of her team's members and asks them the same set of questions. Valerie finds that 83% of her employees rate her performance as "outstanding." Which of these is the best explanation for why this result is probably biased?
Employees may not want to give critical feedback in person to their manager, so this is likely an overestimate of Valerie's performance. *Employees who don't want to give critical feedback might rate her performance more favorably than they really feel. In contrast, it's less likely for employees to rate her performance as worse than they really feel, so 83% is probably an overestimate of her performance.
A large bakery produces cakes in an assembly line. Sergio noticed a potential defect that seems to be showing in every other cake. He decides that in the next production run, he'll take a random sample of cakes to get a better idea of how many cakes might have this defect. Why might Sergio choose a simple random sample instead of a systematic random sample?
If the defect is in every other cake, a systematic random sample could miss it completely depending on what Sergio chooses for k. *Suppose he starts with the 8th cake and k=10. He would pick cakes 8, 18, 28, 38. If the defect is in every other cake starting with the cake 1, then none of the cakes in Sergio's sample would have the defect.
A company wants to study the effectiveness of a new pain relief medicine. They recruit 100 volunteers with chronic pain. Each subject takes the new pain relief medicine for a 2-week period, and a placebo for another 2-week period. Subjects don't know which pill is the actual medicine, and the order of the pills is randomly assigned for each subject. Researchers will measure the difference in the overall pain level for each subject. What type of experiment design is this?
Matched pairs *Each subject took both the new medicine (treatment) and placebo (control), so this study used a matched pairs design.
A group of researchers wants to study the effect of listening to music at different volumes on driving reaction times. They recruit 100 volunteers. While music plays in the car at one of two volume levels, each subject encounters a number of signs, some of which require braking, and their reaction times are recorded. The subjects repeat the experiment at the other volume level. The order of the conditions is randomly assigned for each subject. What type of experiment design is this?
Matched pairs *Each subject took the test with both volume levels, so this study used a matched pairs design.
A mobile phone service provider wants to survey its customers to study privacy concerns and the sharing of their personal information. They call 5000 randomly selected phone numbers from a database containing the phone number of every customer. If someone selected doesn't answer, they'll attempt calling back up to 222 more times before giving up on reaching that person. They reach 350 customers with this strategy, and 60% of those reached say they are at least "somewhat concerned" about their personal information being shared without their knowledge or consent. Which of these is the most concerning potential source of bias in the provider's survey?
Nonresponse bias Nonresponse is when people chosen for the sample can't be contacted or refuse to answer. Only 350 of the 5000 selected were contacted, and it's likely that those who didn't answer repeated calls care about their privacy.
A survey of over 7000 randomly selected employees in 15 nations recently showed that employees who work in a digital workplace tended to be happier than those who don't work in a digital workplace. Can we conclude that working in a digital workplace caused employees to be happier? Why?
Not necessarily, because this wasn't an experiment
Researchers studying meditation contacted over 1000 randomly selected adults in 10 nations. The results showed that those who meditated on a regular basis were less likely to suffer from stress than adults who meditate less regularly or not at all. Can we conclude that meditating caused the lower stress? Why?
Not necessarily, because this wasn't an experiment
Researchers were interested in the relationship between farmers' approach to their cows and the cows' milk yield. After surveying a random sample of 120 farmers, the researchers found that on farms where cows were called by name, milk yield was 258 liters higher on average than on farms where this was not the case. Can we conclude that calling the cows by name caused the cows to produce more milk? Why?
Not necessarily, because this wasn't an experiment
Kara, who lives in Canada, plays a popular online video game where every round has a winner. Her best streak is 21 wins in a row, and she wonders how that compares to other players. The game's website has a worldwide leaderboard of players with the longest win streaks for each month. Kara finds that the top 200 longest streaks in the world in June had an average of about 63 wins in a row. For which population is 63 wins a legitimate estimate of the average longest streak?
Only the top 200 longest streaks worldwide in June *The 200 longest streaks weren't randomly selected from a larger population. They are not representative of all players in the world or Canada—they are the top 200 longest streaks of all players.
A company that recently changed its slogan is hosting an optional company picnic. Some members of the marketing team are eating together at the picnic and sharing their thoughts on the new slogan. They find that 80%, percent of them like the new slogan. For which population is 80%, percent a legitimate estimate of the percent of employees who like the new slogan?
Only those members of the marketing team eating together at the picnic *The members of the marketing team eating together at the picnic weren't randomly selected from a larger population. They may not be representative of employees (marketing team or not) beyond their group.
A news program invites its viewers to call in and share their position on a proposed tax increase. Ninety percent of the viewers that call in say that they will vote against the tax increase. For which population is 90%, percent a legitimate estimate of the percent of voters who will vote against the tax increase?
Only those viewers who called in *The viewers who called in weren't randomly selected, and they are likely not representative of any larger group. Viewers who took the time to call in likely have stronger opinions than those who didn't call in, or different opinions than those who don't watch this show.
Alejandro owns a restaurant where he sells pizza by the slice. He wonders if customers prefer their pepperoni on top of the cheese or under the cheese. Every day for a week, he prepares both types of pizza. Every time a customer orders a slice of pepperoni pizza, he flips a coin to determine whether he'll give the customer a slice with pepperoni on top or under the cheese. He then asked each customer to rate their pizza. At the end of the week, he found that customers who received pepperoni on top rated their pizza significantly better on average than customers who received pepperoni under the cheese. What conclusion can they draw from this study?
Pepperoni placement caused the difference in customer ratings
A grocery store wonders if their sales will be better if they play ambient music or no music at all. Each day for 2 months, the manager flips a coin to determine whether or not the store will play music that day. At the end of the 2 months, the manager finds that, on average, sales were significantly better on days where music was playing. What conclusion can they draw from this study?
Playing music caused better sales.
A professor wants to study the effectiveness of a new study tool for a course. There are 150 students registered for the course. Half of the freshmen are randomly assigned to use the new study tool, and the other half are assigned to use the previous study tool. The same method is used to randomly assign half of the sophomores, half of the juniors, and half of the seniors to each study tool. What type of experiment design is this?
Randomized block *Subjects were divided into groups based on class before being randomly assigned, so this study used a randomized block design.
A company wants to study the effectiveness of a new pain relief medicine. They recruit 100 volunteers who suffer chronic pain. Half of the 50 males are randomly assigned to the treatment group, and the other half are assigned to the control group. The same method is used to randomly assign half of the 50 females to the treatment group and the other half to the control group. What type of experiment design is this?
Randomized block *Subjects were divided into groups based on gender before being randomly assigned, so this study used a randomized block design.
A group of researchers wants to study the effect of listening to music at different volumes on driving reaction times. They recruit 100 volunteers. Half of the subjects with fewer than 10 years of driving experience are randomly assigned to take the test with one music volume, and the other half are assigned to take the test at the other music volume. The same method is used to randomly assign half of the drivers with at least 10 years of driving experience to each testing condition. What type of experiment design is this?
Randomized block *Subjects were divided into groups based on years of experience before being randomly assigned, so this study used a randomized block design.
A concert venue offers tickets in 3 zones: orchestra, grand tier, and balcony. Tickets in the orchestra zone are most expensive, and tickets in the balcony zone are least expensive. Managers of the venue want to survey approximately 150 guests at an upcoming concert about their overall experience. They want to take a systematic random sample of the 3000 guests they expect to attend. Which of these strategies will accomplish their intended design?
Randomly select one of the first 20 guests to arrive and every 20th guest thereafter to take the survey. *3000/20 = 150
Jerome's favorite Harry Potter book has 22 chapters, 500 pages, and approximately 100000 words. He's curious how many of the words are "made up" words or names that don't exist in the dictionary. He wants to take a systematic random sample of about 500 words to estimate what percent of the words in the book are made up. Which of these strategies will accomplish his intended design?
Randomly select one of the first 200 words and every 200th word thereafter for the sample.
A college professor wants to survey a sample of students taking her large lecture course. There are about 150 students in the course, and 10 of those students are graduate students. She wants to take a systematic random sample of approximately 30 students. Which of these strategies will accomplish her intended design?
Randomly select one of the first 5 students to arrive to class, and every 5th student thereafter to take the survey. *This is a systematic sample since the students arrive in some order, she selects the kth student, and then selects every kth student thereafter. Also, 150/5= 30 students.
A manager at a pizza shop wants to start visually checking finished pizzas, but she doesn't have time to check every pizza. She decides to check a random pizza in the first 20 made each day, and then check every 20th pizza thereafter. What type of sample is this?
Systematic random sample
Security workers at an airport randomly choose one of the first 50 people to pass through a checkpoint for extra security screening. After that person, they choose every 50th person who passes through for extra screening as well. What type of sample is this?
Systematic random sample
Lucio wants to know whether the food he serves in his restaurant is within a safe range of temperatures. He randomly selects 70 entrees and measures their temperatures just before he serves them to his customers. Identify the population and sample in this setting.
The population is all of the entrees Lucio serves; the sample is the 70 selected entrees.
Administrators at Riverview High School surveyed a random sample of 100 of their seniors to see how seniors at the school felt about the lunch offering at the school's cafeteria. Identify the population and sample in this setting.
The population is all the seniors at riverview high; the sample is the 100 seniors
The owners of a sports stadium wanted to predict what additional refreshment options would sell well. They selected 80 seat numbers at random and surveyed the occupants of those seats. Identify the population and sample in this setting.
The population is the occupants of all seats in the sports stadium; the sample is the occupants of the 80 selected seats.
A class was curious if their teacher could grade and return double-spaced papers faster than single-spaced papers. For a certain assignment, each student flipped a coin to determine if they would single-space or double-space their paper. The students agreed to all use the same font. The students who double-spaced received their graded papers back significantly faster than students who single-spaced. The class concluded that any teacher can grade and return papers faster if they are double-spaced rather than single-spaced. Why is their conclusion not appropriate?
The study was an experiment, but it didn't include anyone other than their teacher.
There is an ongoing debate about how many spaces should be placed after a period in typed documents. Alana read about a study where 100 participants all read the same document typed in Courier New font. Half of the participants were randomly assigned the document with one space after each period, and the other half were given the document with two spaces after each period. Participants who read the document with two spaces after each period were able to finish reading significantly faster than those with one space after each period. Alana concluded that using two spaces after each period will help people read all documents faster. Why is Alana's conclusion not appropriate?
The study was an experiment, but it didn't include fonts other than Courier New.
Diego read a medical research study about the connection between type 2 diabetes and walnut consumption. The study looked at dietary and disease patterns in a sample of over 30,000 American adults, and it found that those who consumed more walnuts were significantly less likely to have type 2 diabetes. Diego concluded that eating more walnuts would make him less likely to get type 2 diabetes. Why is Diego's conclusion not appropriate?
The study was observational, so he shouldn't make a causal conclusion.
A surgeon developed a new procedure for knee replacement surgery. To study its effectiveness, they recruit patients who need knee replacement surgery and are willing to participate in a blind study. The surgeon randomly assigns each volunteer to receive either the new procedure or the standard procedure. After the surgeon performs the procedure, they monitor each patient to see if one group has better results than the other. What does it mean for this experiment to be blind?
The volunteers are unaware of which surgery they receive. *This refers to regular blinding since the subjects are unaware of who is in which group.
The superintendent of a large school district is curious about the relationship between students' grades and their participation in extracurricular activities. They take a random sample of 500 students and find that students with more participation in extracurricular activities are far more likely to have high grades than students with little or no participation. What conclusion can they draw from this study?
There was an association between extracurricular participation and grades, but it's not necessarily a causal relationship.
A recent study examined 323 healthy women who wore watch-like devices that tracked their sleep each night. The women with sleep problems (difficultly falling asleep and waking up throughout the night) were significantly more likely to have high blood pressure than women without those sleep problems. What conclusion can they draw from this study?
There was an association between sleep problems and high blood pressure, but it's not necessarily a causal relationship.
A store prints a request on each receipt asking customers to fill out a satisfaction survey online if they are willing.
Voluntary response sample
A company makes a bracelet that is designed to repel mosquitos so people don't have to wear bug spray. Researchers at the company are designing an experiment where volunteers will be assigned either the bracelet or bug spray to use at their homes. The researchers want to use a randomized block design. How should the researchers form the blocks?
Volunteers within each block should live in similar environments to each other when it comes to mosquitos. *They should block volunteers based on variables they know might impact the results of the experiment—like how many mosquitos are in a given environment. Members of each block should live in a similar environment to each other, so some volunteers in each environment will use the bracelet and some will use the bug spray.
Andrey works at a call center, selling insurance over the phone. While debating which greeting he should use when calling potential customers — "Howdy!" or "Hiya!" — he decided to conduct a small study. For his subsequent 500 calls, he chose one of the greetings randomly by flipping a coin, and used the same script for his sale otherwise. Then, he compared the percentage of calls he succeeded in selling insurance using each greeting. He noticed that he was significantly more likely to make a sale in calls that started with "Hiya!" Can we conclude that the greeting caused the difference in sales? Why?
Yes, because the calls were each randomly assigned a greeting
Roshanda was curious if students in her class would complete a maze faster if fast-paced music was playing in the background. She randomly assigned each student in her class to one of three groups: fast-paced music, slow-paced music, or no music. She timed each student as they individually completed a maze with their corresponding music (or no music) in the background. Students who worked with the fast-paced music, on average, completed the maze significantly faster than students in the other groups. Can we conclude that the fast-paced music caused her classmates to finish the maze faster? Why?
Yes, because the students were randomly assigned to treatment and control groups