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Scope of inference

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54662312

A factory selects a simple random sample of items produced during a shift and records whether each item is defective. No treatment is imposed. What scope of inference is justified by the sample defect rate?

Hints

- Use the random sample to identify the population. - Determine whether any explanatory treatment was assigned. - Separate estimating a rate from explaining why it occurs.

Solution

1. Random selection permits estimation of the defect proportion for all items produced during that shift. 2. The study is descriptive and observational. 3. It can support generalization about the production population but no causal conclusion about why defects occurred.

Answer

The sample defect rate may be generalized to estimate the defect proportion among all items produced during that shift. The study does not identify causes of defects.

54655312

A university takes a simple random sample of first-year students and randomly assigns each selected student to receive either a standard advising email or a redesigned email. The response is whether the student schedules an advising appointment. What conclusions would a statistically significant difference support?

Hints

- Identify the role of the random sample. - Identify the separate role of random assignment. - Combine the two permissions in the final conclusion.

Solution

1. Random selection supports generalization to all first-year students at the university. 2. Random assignment supports a cause-and-effect conclusion about the email design. 3. Therefore, the study can estimate a causal effect for the university's first-year student population.

Answer

The university may generalize the result to all of its first-year students and conclude that the email design caused the difference in appointment-scheduling rates.

54656312

A sleep laboratory recruits volunteers who regularly use wearable devices. The volunteers are randomly assigned to receive either a new sleep-feedback display or the standard display. The new display improves reported sleep habits. State the strongest justified conclusion.

Hints

- Determine what random assignment allows. - Examine whether the participants were randomly selected from a defined population. - Restrict the conclusion to the people actually represented by the recruitment process.

Solution

1. Random assignment supports a causal conclusion about the display for the participants in the experiment. 2. Volunteer recruitment does not support statistical generalization to all adults or another defined population. 3. Therefore, the strongest conclusion concerns only the participants studied.

Answer

The new display caused improved reported sleep habits among the volunteers who participated in the experiment. The result should not be statistically generalized to all adults.

54656812

A county selects a simple random sample of registered voters and records whether each voter attended a public meeting and whether the voter supports a proposed bond. Support is higher among meeting attendees. What may the county infer?

Hints

- Use the sampling method to determine the population scope. - Decide whether attendance was imposed as a treatment. - Phrase the relationship as association unless causation is justified.

Solution

1. Random selection permits generalization to the population of registered voters in the county. 2. Meeting attendance was observed, not assigned. 3. The result supports an association between attendance and bond support in that population. 4. It does not show that attending a meeting causes support.

Answer

The county may generalize the association to all registered voters in the county. It may not conclude that attending a public meeting causes greater support for the bond.

54657812

A corporation takes a simple random sample of its remote employees and randomly assigns those employees to one of two meeting schedules for a month. Productivity is higher under Schedule B. State the full scope of inference.

Hints

- Determine what the random sample permits. - Determine what the random assignment permits. - State the population and the causal relationship together.

Solution

1. Random selection permits generalization to all remote employees at the corporation. 2. Random assignment permits a cause-and-effect conclusion. 3. The study supports the conclusion that Schedule B causes higher productivity for the corporation's remote-employee population.

Answer

The corporation may conclude that Schedule B caused higher productivity and generalize that causal conclusion to all of its remote employees.

54658812

A state takes a simple random sample of public schools and compares schools that already use later start times with schools that use earlier start times. Schools with later starts have higher attendance. What conclusions are justified?

Hints

- Use the school-selection process to decide the population scope. - Decide whether researchers imposed the start times. - State association and causation conclusions separately.

Solution

1. Random selection of schools permits generalization to the state's public schools. 2. Start time was not randomly assigned by the researchers. 3. The study supports a statewide association between start time and attendance. 4. It does not establish that later start times cause higher attendance.

Answer

The association may be generalized to public schools in the state. A cause-and-effect conclusion is not justified because start times were observed rather than randomly assigned.

54659312

Researchers recruit only adults ages \(65\) to \(75\) from two senior centers and randomly assign them to two balance-training programs. Program A reduces falls more than Program B. State the appropriate scope of inference.

Hints

- Identify what random assignment permits. - Examine the narrow age and recruitment setting. - State the most defensible population represented by the participants.

Solution

1. Random assignment supports a cause-and-effect conclusion between training program and falls for the participants. 2. The participants were recruited from two senior centers and were not randomly selected from a larger population. 3. Therefore, the study does not support statistical generalization beyond the participants.

Answer

Program A caused fewer falls among the participants studied. The result should not be statistically generalized to all older adults or to other age groups.

54660312

A researcher asks visitors at one comic convention whether costume participation is related to social confidence. Participants volunteer at a booth, and no treatment is assigned. What is the strongest conclusion the researcher may report?

Hints

- Examine how people entered the study. - Decide whether a treatment was imposed. - Limit both the population and relationship claims to what the design supports.

Solution

1. The booth respondents form a voluntary, nonrandom sample from one convention. 2. The variables are observed rather than assigned. 3. The researcher may describe an association among respondents. 4. The result does not support broad generalization or causation.

Answer

The researcher may report an association among the people who volunteered at that convention. The study does not justify generalizing to all convention visitors or concluding that costume participation causes greater social confidence.

54660812

An electronics company randomly samples circuit boards from one day's production and randomly assigns the sampled boards to two inspection procedures. Procedure B finds more defects. What conclusions are justified?

Hints

- Identify the population from which boards were randomly selected. - Identify the role of random assignment to inspection procedures. - State the causal effect for the correct production population.

Solution

1. Random sampling permits generalization to all circuit boards produced that day. 2. Random assignment permits a causal comparison of the inspection procedures. 3. The company may conclude that Procedure B causes a higher defect-detection rate for boards from that day's production.

Answer

The company may conclude that Procedure B causes more defects to be detected and generalize that causal conclusion to all circuit boards produced that day.

54662812

A wildlife agency takes a simple random sample of deer observed in one protected area during winter and estimates average body mass. How far may the result be generalized?

Hints

- Define the population using both place and time. - Use the sampling frame, not the broader species name, to set the boundary. - Avoid extending the result beyond units that could have been selected.

Solution

1. The random sample represents deer in the defined sampling population: the protected area during winter under the observation frame. 2. It does not automatically represent deer in other areas or seasons. 3. The estimate may be generalized only to the population from which the random sample was selected.

Answer

The estimate may be generalized to deer in that protected area during the winter sampling period that were included in the observation frame. It should not automatically be generalized to unobserved deer, other areas, other seasons, or other deer populations.

54663312

A streaming service takes a simple random sample of subscribers and randomly assigns them to two recommendation-page layouts. One layout increases the proportion who start a new series. State the strongest conclusion.

Hints

- Identify the permission created by random selection. - Identify the separate permission created by random assignment. - State the causal effect for the correct subscriber population.

Solution

1. Random selection permits generalization to all subscribers represented by the sampling frame. 2. Random assignment permits a causal conclusion about layout. 3. The service may conclude that the layout causes a change in the start rate for that subscriber population.

Answer

The service may conclude that the layout caused the difference in new-series starts and generalize that causal effect to all subscribers represented by the random sample.

54663812

People who attend one weekend cooking expo volunteer for a study and are randomly assigned to watch either a short food-safety video or no video. The video group answers more safety questions correctly. State the scope of inference.

Hints

- Use random assignment to evaluate causation. - Use recruitment to evaluate population generalization. - Name the narrow group represented by the volunteers.

Solution

1. Random assignment supports a causal conclusion about the video for the participants. 2. Volunteer expo attendees are not a random sample of the general public. 3. Therefore, the study does not support statistical generalization beyond the participants.

Answer

The video caused higher food-safety scores among the participants. The result should not be statistically generalized to the general public.

54664312

A library takes a simple random sample of its cardholders and finds that people who attend library programs borrow more books. State the strongest inference.

Hints

- Use the sampling method to identify the population. - Ask whether attendance was assigned by researchers. - Phrase the conclusion as association unless a causal design was used.

Solution

1. Random sampling supports generalization to all cardholders of that library. 2. Program attendance was observed rather than assigned. 3. The study supports an association between attendance and borrowing. 4. It does not show that program attendance causes more borrowing.

Answer

The association may be generalized to all cardholders of that library, but the library cannot conclude that attending programs causes people to borrow more books.

54665312

An online hobby forum invites members to report weekly practice time and current skill level. The analysis finds that more practice is associated with higher skill. State the scope of inference.

Hints

- Examine how members entered the data set. - Decide whether practice time was imposed. - Limit both the population and causal claims.

Solution

1. Respondents volunteer from one online forum, so the sample is nonrandom. 2. Practice time is observed rather than assigned. 3. The association can be described for the forum members who responded. 4. It cannot be statistically generalized to a broader population or interpreted as proof that more practice caused the skill difference.

Answer

The study supports an association among the forum members who responded. It does not justify broad population generalization or a causal conclusion.

54666812

A neighborhood association takes a simple random sample from its membership list and estimates support for a zoning proposal. May the result be generalized to all neighborhood residents? Explain.

Hints

- Identify exactly who could be selected. - Compare the sampling frame with the population named in the proposed conclusion. - Limit generalization to the frame represented by the random sample.

Solution

1. The random sample represents the population on the membership list. 2. Residents who are not association members had no chance of selection. 3. Therefore, the result may be generalized to association members but not automatically to all neighborhood residents.

Answer

No. The result may be generalized to association members, not to all neighborhood residents, because nonmembers were outside the sampling frame.

54667812

A social platform analyzes every active account during one week and finds that accounts following more news sources also share more articles. State the scope of inference.

Hints

- Define the complete population included in the records. - Ask whether the explanatory variable was assigned. - Keep time and account-status limits in the conclusion.

Solution

1. The data form a census of active accounts during that week. 2. The association describes that account population and time period. 3. Number of followed sources was not randomly assigned. 4. The analysis does not show that following more sources causes more sharing or apply automatically to inactive accounts or other weeks.

Answer

The association applies to all active accounts during the week studied. It does not establish causation and should not automatically be extended to inactive accounts or different time periods.

54668812

A city takes a simple random sample of signalized intersections. Each selected intersection is randomly assigned either a standard pedestrian signal or a new countdown signal for six weeks. The new signals reduce the mean number of pedestrians entering after the warning begins. State the strongest conclusion.

Hints

- Identify separately how intersections were selected and how signal types were assigned. - Connect one random process to generalization and the other to causation. - State the conclusion using the measured response and the intended population.

Solution

1. Random assignment supports a cause-and-effect conclusion about the signal type. 2. Random selection of intersections supports generalization from the sampled intersections to all signalized intersections in the city. 3. The study therefore supports that installing the new countdown signal would reduce the mean number of late-entering pedestrians at the city's signalized intersections.

Answer

The city may conclude that the new countdown signal causes a reduction in the mean number of pedestrians who enter after the warning begins, and it may generalize that conclusion to all signalized intersections in the city.

54680112

A medical center takes a simple random sample of patients age \(65\) or older and randomly assigns two appointment-scheduling systems. System B reduces missed appointments. State the strongest conclusion and explain the age limitation.

Hints

- Use treatment assignment to determine whether causation is supported. - Define the population from the eligibility rule used before sampling. - Identify the age group that had no chance to enter the study.

Solution

1. Random assignment supports a causal conclusion that System B reduces missed appointments. 2. Random selection supports generalization to the population of patients age \(65\) or older represented by the center's sampling frame. 3. No patients younger than \(65\) were included in the frame. 4. Therefore, the result should not automatically be generalized to younger patients.

Answer

System B causes fewer missed appointments among patients age \(65\) or older represented by the sampling frame. The study does not establish the same effect for younger patients.

54680612

A national charter-school network takes a simple random sample of its teachers and randomly assigns two online training formats. Format A produces higher mean assessment scores. State the strongest conclusion and explain why it does not extend automatically to all U.S. teachers.

Hints

- Use assignment to decide whether the format can be treated as a cause. - Define the population from the roster used for random selection. - Identify educators who were outside that roster.

Solution

1. Random assignment supports a causal conclusion that Format A raises mean assessment scores. 2. Random selection supports generalization to teachers in the charter-school network represented by the sampling frame. 3. Teachers outside that network, including teachers in other public and private schools, had no chance to be selected. 4. The result therefore does not automatically generalize to all U.S. teachers.

Answer

Format A causes higher mean assessment scores among teachers represented by the charter-school network's sampling frame. The study does not automatically generalize to all U.S. teachers.

54681612

A publishing company takes an SRS of \(120\) of its current remote proofreaders. The proofreaders are randomly assigned to work with either noise-canceling headphones or their usual equipment for one week. The headphone group makes fewer proofreading errors. State the population and causal scope of the conclusion.

Hints

- Identify the group from which participants were selected by chance. - Identify the condition that was assigned by chance. - Keep the conclusion within the job, organization, and duration actually studied.

Solution

1. Random selection supports generalization to the company’s current remote proofreaders. 2. Random assignment supports a causal conclusion about using the headphones under the tested one-week work conditions. 3. The study does not automatically generalize to other occupations, companies, or longer-term use.

Answer

For the company’s current remote proofreaders, using the noise-canceling headphones caused fewer proofreading errors during the tested week. The conclusion does not automatically extend to other workers, companies, or longer periods.

54843012

A festival organizer selects a simple random sample of \(250\) people from a list of \(5000\) attendees who entered before noon. Of those sampled, \(145\) arrived by public transportation. An analyst proposes constructing a confidence interval for the proportion of all festival attendees who arrived by public transportation. a) Identify the population for which a standard one-proportion confidence interval is supported by this sample. b) Explain why the proposed interval does not automatically apply to all festival attendees. c) State what additional sampling design would support inference to all attendees.

Hints

- Identify exactly who had a chance to be selected. - Match the target population of an interval to the sampling frame. - Consider how the sampling design would need to change to include the omitted group.

Solution

1. The random sample was drawn from the \(5000\) attendees who entered before noon. Also, \(250\le0.10(5000)=500\), and the observed counts are \(145\) and \(105\), both at least \(10\). Therefore, the supported population is all attendees who entered before noon. 2. Later-arriving attendees had no chance to be selected. Their transportation choices could differ, so the sample is not a random sample of all festival attendees. 3. To support inference to all attendees, the organizer should select a random sample from a complete list or sampling frame that covers attendees throughout the festival.

Answer

a) All festival attendees who entered before noon. b) Attendees arriving at noon or later were excluded from the sampling frame, so the sample is not representative by design of all attendees. c) Use a random sample from a frame that includes every festival attendee, or a design that randomly samples across the full arrival period.

54850212

A professional association asks every one of its \(420\) current members whether they favor a proposed dues change. All \(420\) members respond, and \(231\) favor the change. Should the association construct a confidence interval for the proportion of its current members who favor the change? State the relevant proportion and explain.

Hints

- Identify whether the data come from a sample or from every member of the stated population. - Decide what source of uncertainty a confidence interval is intended to describe. - Keep the target population limited to the group named in the question.

Solution

1. The association observed the entire target population of current members, not a sample from that population. 2. The population proportion is known exactly: \(p=\frac{231}{420}=0.55\). 3. A confidence interval for sampling uncertainty is unnecessary because there is no random sampling error for this finite target population.

Answer

No confidence interval is needed for the current membership. The exact proportion is \(0.55\), or \(55\%\), because every current member was included.

54653812

A grocery chain takes a simple random sample of receipts from all purchases made at its stores during one month. For each receipt, it records checkout waiting time and the customer's satisfaction rating. The data show that longer waits are associated with lower ratings. State the strongest conclusions supported by the study.

Hints

- Separate how the observational units were selected from how the explanatory variable arose. - Decide whether the study supports population generalization. - Decide independently whether it supports causation.

Solution

1. Random selection permits generalization from the sampled receipts to all purchases made by the chain during that month. 2. Waiting time was observed rather than randomly assigned. 3. The study supports an association but not a cause-and-effect conclusion.

Answer

The chain may generalize the observed association to all of its purchases during that month. It cannot conclude that longer waits cause lower satisfaction because there was no random assignment of waiting times.

54654312

Researchers recruit volunteers from one fitness center and randomly assign them to either a new interval-training plan or the center's usual plan. After eight weeks, the interval group has a larger mean improvement in endurance. What cause-and-effect and population conclusions are justified?

Hints

- Evaluate random assignment and random selection separately. - Link random assignment to the type of relationship that can be concluded. - Limit the population conclusion to the people actually represented by the recruitment process.

Solution

1. Random assignment supports a cause-and-effect conclusion for the participants in the experiment. 2. The participants were volunteers from one fitness center rather than a random sample from a broader population. 3. Therefore, the result cannot be statistically generalized to all adults or to another defined population.

Answer

The study supports the conclusion that the interval-training plan caused greater mean endurance improvement among the participants in this experiment. It does not justify generalizing the result to all adults because the participants were volunteers from one fitness center.

54654812

A basketball league records minutes played and number of ankle injuries for every player during one complete season. Players with more minutes tend to have more injuries. Describe the scope of inference.

Hints

- Decide whether the data came from a sample or the entire stated population. - Ask whether the explanatory variable was imposed by researchers. - Keep description of a relationship separate from a causal claim.

Solution

1. Because data were collected for every player in that league season, the result describes that full population rather than estimating from a sample. 2. Playing time was not randomly assigned as a treatment. 3. The observed relationship is an association and does not establish that additional minutes cause injuries.

Answer

The association applies to all players in that league during the season studied because the data form a census of that population. A cause-and-effect conclusion is not justified.

54655812

A researcher interviews people leaving one downtown farmers market and finds an association between buying local food and reporting high concern about climate change. The people interviewed were the first sixty willing participants. State the appropriate scope of inference.

Hints

- Examine how participants entered the sample. - Identify the group for which data were actually collected. - Ask whether either variable was imposed as a treatment. - State generalization and causation limits separately.

Solution

1. The sample was a convenience sample of willing people at one location. 2. The result cannot be generalized to all city residents, all farmers-market customers, or another defined population. 3. The variables were observed rather than assigned. 4. The study supports an association only among the sixty people interviewed, not a cause-and-effect conclusion.

Answer

The study supports an association only among the sixty willing people interviewed at that market. It does not support statistical generalization to a broader population or a claim that buying local food causes greater climate concern.

54657312

Six volunteer high schools participate in a study. Within each school, classes are randomly assigned to use either a new discussion routine or the usual routine. The new routine produces higher participation scores. Describe the justified causal and population conclusions.

Hints

- Identify the unit that was randomly assigned. - Separate the causal conclusion from the population conclusion. - Examine how the schools entered the study.

Solution

1. Random assignment of classes supports a causal conclusion about the routine for the participating classes. 2. The schools volunteered and were not randomly selected from a larger population. 3. Therefore, the study does not support statistical generalization beyond the participating schools and classes.

Answer

The new routine caused higher participation scores among the participating classes. The result should not be statistically generalized to all high schools because the schools were volunteers rather than a random sample.

54658312

A company analyzes payroll and commute records for every employee at its headquarters. Employees with longer commutes have higher average absenteeism. What can the company conclude about scope and causation?

Hints

- Identify the exact population included in full. - Ask whether commute length was imposed by researchers. - Keep conclusions about other company locations separate from this census.

Solution

1. The data cover every employee at that headquarters, so the association describes that complete employee population. 2. Commute length was observed rather than assigned. 3. The company cannot conclude that longer commutes cause more absences because confounding explanations remain possible.

Answer

The company may state that commute length and absenteeism are associated among all employees at that headquarters. It may not claim that longer commutes cause higher absenteeism or generalize automatically to employees at other locations.

54659812

A county takes a simple random sample of households and compares households that chose rooftop solar panels with households that did not. Solar households report lower electricity bills. State the appropriate scope of inference.

Hints

- Use the household selection method to determine the population. - Ask whether solar adoption was imposed by researchers. - Allow for alternative explanations when treatment is self-selected.

Solution

1. Random sampling supports generalization to households in the county. 2. Solar adoption was self-selected, not randomly assigned. 3. The study supports an association between solar adoption and electricity bills in the county. 4. It does not establish that installing solar panels caused the full observed difference.

Answer

The association may be generalized to county households. A causal conclusion is not justified because households chose whether to install solar panels, so other differences may explain part of the bill difference.

54661312

Researchers randomly sample adults from a county and use medical records from the previous ten years to compare those with high and low long-term air-pollution exposure. Higher exposure is associated with more respiratory diagnoses. State the scope of inference.

Hints

- Use the random sample to identify the population. - Determine whether the exposure was imposed or found in past records. - Account for alternative explanations when stating the relationship.

Solution

1. Random sampling supports generalization to adults in the county. 2. The study is retrospective and observational because past exposure was not assigned. 3. The result supports a countywide association. 4. It does not establish that pollution exposure caused the diagnoses because confounding variables may exist.

Answer

The association may be generalized to adults in the county. The retrospective observational design does not justify a cause-and-effect conclusion.

54664812

A corporation randomly samples work teams from all of its domestic offices and randomly assigns each sampled team to one of two collaboration tools. Tool B improves team output. State the scope of inference.

Hints

- Keep the unit of inference consistent with the unit sampled and assigned. - Use random selection for generalization. - Use random assignment for causation.

Solution

1. Random sampling of teams supports generalization to domestic work teams represented by the frame. 2. Random assignment of tools supports a cause-and-effect conclusion at the team level. 3. The corporation may infer that Tool B causes higher team output for its domestic teams.

Answer

The corporation may conclude that Tool B causes higher output and generalize that causal effect to its domestic work teams represented by the random sample.

54665812

A state randomly samples driver's-license records and compares crash rates for drivers who did and did not complete an optional defensive-driving course. Course participants have fewer crashes. State the scope of inference.

Hints

- Use record selection to set the population scope. - Determine whether course participation was assigned. - Allow for preexisting differences between participants and nonparticipants.

Solution

1. Random sampling supports generalization to licensed drivers represented by the state records. 2. Course participation was optional, not randomly assigned. 3. The study supports a population association. 4. It does not prove that the course caused the lower crash rate because participants may differ in other ways.

Answer

The association may be generalized to the state's licensed drivers represented by the records. A causal conclusion is not justified because course participation was self-selected.

54666312

A city records every reported bicycle crash during one calendar year and finds that crashes are more common on streets without bike lanes. Describe the scope of inference.

Hints

- Define the population using the record system, place, and time. - Ask whether street features were assigned by researchers. - Notice which events never enter the records.

Solution

1. The records form a census of reported crashes in the city during that year. 2. The finding describes that recorded crash population. 3. Street type was not randomly assigned. 4. The study does not establish that the absence of bike lanes caused the higher crash frequency, and unreported crashes are outside the data.

Answer

The association describes reported bicycle crashes in that city during the year studied. It does not establish causation and does not automatically include unreported crashes or other years and cities.

54667312

Volunteer farms participate in a study, and plots within each farm are randomly assigned to two irrigation schedules. Schedule A increases crop yield. State the justified scope of inference.

Hints

- Identify the unit receiving random assignment. - Examine how farms entered the study. - State causation and population scope separately.

Solution

1. Random assignment of plots supports a causal conclusion about irrigation schedule for plots in the participating farms. 2. The farms volunteered rather than being randomly sampled from a larger population. 3. Therefore, the study does not support statistical generalization beyond the participating farms.

Answer

Schedule A caused higher yield for the plots studied in the participating farms. The causal result should not be statistically generalized to all farms.

54668312

A state agency takes a simple random sample of counties in the state. For each selected county, it records the type of emergency-alert system already in use and the median time residents took to begin evacuating during the county's most recent wildfire. Counties using phone alerts had shorter median evacuation times. State the strongest conclusion supported by the study.

Hints

- Separate how the counties entered the study from how the alert systems were chosen. - Ask whether random selection supports generalization. - Ask whether the explanatory condition was imposed by the researchers.

Solution

1. The counties were randomly selected, so the observed association may be generalized to counties in the state. 2. The alert systems were not randomly assigned; the agency observed systems already in use. 3. Therefore, the study supports an association between phone alerts and shorter median evacuation times for counties in the state, but it does not establish that phone alerts caused the difference.

Answer

The results support a statewide association: counties using phone alerts tend to have shorter median evacuation times. Because the alert systems were not randomly assigned, a cause-and-effect conclusion is not justified.

54669312

A manufacturer takes a simple random sample of rechargeable batteries from one production lot and randomly assigns them to two charging protocols. After \(100\) charge cycles, Protocol B produces a higher mean remaining capacity. State the strongest conclusion and one limitation concerning time.

Hints

- Use the selection process to determine the population scope. - Use the assignment process to determine whether causation is supported. - Keep the conclusion tied to the exact response and time point that were measured.

Solution

1. Random assignment supports a causal conclusion that the charging protocol affects remaining capacity after \(100\) cycles. 2. Random selection from the lot supports generalization to all batteries in that production lot. 3. Because the response was measured after \(100\) cycles, the study does not establish which protocol gives greater capacity after substantially more cycles or over the full battery life.

Answer

For batteries in this production lot, Protocol B causes a higher mean remaining capacity after \(100\) charge cycles. The result does not establish a long-term advantage beyond the measured \(100\)-cycle period.

54670812

Two studies evaluate a new budgeting app. Study I takes a simple random sample of all customers and compares people who chose to use the app with people who did not. Study II recruits volunteers and randomly assigns them either to receive the app or not receive it. For each study, state whether it supports generalization to all customers and whether it supports a cause-and-effect conclusion.

Hints

- Analyze participant selection separately from treatment assignment. - Connect random selection with the population represented. - Connect random assignment with whether the explanatory condition can be treated as a cause.

Solution

1. Study I uses random selection, so its observed association may be generalized to all customers. Because app use is self-selected, it does not establish causation. 2. Study II uses random assignment, so it can establish a causal effect of receiving the app among the participants. Because the participants were volunteers rather than a random sample, it does not support statistical generalization to all customers.

Answer

Study I: generalization to all customers is supported; causation is not. Study II: causation is supported for the participants; generalization to all customers is not.

54671312

A call center takes a simple random sample from all completed customer-support calls in June. It finds that calls using an interpreter have longer resolution times than calls not using an interpreter. State the population to which the result may be generalized and explain why the study does not establish causation.

Hints

- Define the population from the exact list used for random selection. - Notice which calls never had a chance to appear in that list. - Ask whether the explanatory condition was imposed by the researchers.

Solution

1. The sampling frame contains completed customer-support calls in June, so random selection supports generalization to that population of calls. 2. Calls that were abandoned or never completed are outside the sampled population. 3. Interpreter use was observed rather than randomly assigned. 4. Differences in issue complexity, language needs, or customer circumstances could explain the longer times, so causation is not supported.

Answer

The association may be generalized to completed customer-support calls in June, not to abandoned or other calls outside that frame. Because interpreter use was not randomly assigned, the study does not show that using an interpreter caused longer resolution times.

54672812

An online retailer takes a simple random sample of customers and randomly assigns two email subject lines. Subject Line B causes a higher email-open rate. The retailer did not measure purchases. State the strongest conclusion and explain why a sales conclusion is not justified.

Hints

- Tie the causal conclusion to the response actually recorded. - Use the random sample to determine the population scope. - Separate a measured intermediate behavior from an unmeasured business outcome.

Solution

1. Random assignment supports a causal conclusion about the measured response, email opening. 2. Random selection supports generalization to the retailer's customer population represented by the sampling frame. 3. The study supports that Subject Line B increases the probability of opening the email for that population. 4. Because purchase behavior was not measured, the study does not establish that Subject Line B increases sales or purchase rates.

Answer

Subject Line B causes a higher email-open rate for the customer population represented by the random sample. No conclusion about purchases or sales is supported because those outcomes were not measured.

54673812

An app company takes a simple random sample of user sessions recorded in 2025 and finds that sessions begun from push notifications have shorter duration than sessions begun directly. The app interface and notification system were redesigned in 2026. State the justified scope of inference.

Hints

- Define the population using the time period in the sampling frame. - Determine whether the explanatory variable was assigned or merely recorded. - Consider whether a later system change makes the old population comparable to the new one.

Solution

1. Random selection supports generalization to the 2025 user sessions represented by the sampling frame. 2. Session entry method was observed rather than randomly assigned, so only an association is supported. 3. The redesign may have changed user behavior and the meaning of the entry categories. 4. Therefore, the result should not automatically be generalized to 2026 sessions under the redesigned system.

Answer

The study supports an association between entry method and session duration for the 2025 sessions represented by the sample. It does not establish causation and should not automatically be generalized to sessions after the 2026 redesign.

54674812

A regional company includes all \(12\) of its current branches in an experiment and randomly assigns each branch to one of two inventory systems. System B reduces the mean number of order errors. State the strongest conclusion and explain the limit on generalization.

Hints

- Determine whether the study used all units in a defined finite population. - Use random assignment to decide whether causation is supported. - Identify broader groups that were not represented through random selection.

Solution

1. Random assignment of branches supports a causal conclusion that System B reduces the mean number of order errors for the \(12\) participating branches under the study conditions. 2. Because all current branches were included, no sampling inference is needed for that finite set. 3. The branches were not randomly sampled from a broader population of possible or future branches. 4. The result should not automatically be generalized to future branches, branches in other regions, or substantially different operating conditions.

Answer

System B causes a lower mean number of order errors for the company's \(12\) current branches under the study conditions. The study does not by itself support generalization to future branches or branches outside this regional company.

54675212

One state adopts a new road-safety law, while a neighboring state does not. Researchers compare crash rates in the two states after the change and find a larger decrease in the adopting state. No states were randomly selected or assigned. State the justified scope of inference.

Hints

- Check whether the policy was assigned by a random mechanism. - Check whether the states were sampled from a larger population. - Keep the conclusion limited to the states and period actually observed.

Solution

1. The policy condition was not randomly assigned, so differences between the states provide alternative explanations for the crash-rate change. 2. The study does not establish that the law caused the larger decrease. 3. Because only these two deliberately chosen states were studied, the result does not support broad statistical generalization to other states. 4. The appropriate conclusion is a descriptive association for the two states during the studied period.

Answer

The study shows that the adopting state had a larger crash-rate decrease than the comparison state during the studied period. It does not establish causation and does not support generalization to other states.

54677212

A health system takes a simple random sample of adult patients and records whether each patient has a particular genetic marker and whether the patient has a certain condition. The marker is associated with higher condition prevalence. State the strongest inference.

Hints

- Use the sampling process to set the population scope. - Ask whether researchers imposed the explanatory condition. - Phrase the conclusion as a relationship rather than an intervention effect.

Solution

1. Random selection supports generalizing the association to adult patients in the health-system population represented by the sampling frame. 2. The genetic marker was observed rather than assigned by researchers. 3. The study supports an association between the marker and condition prevalence. 4. It does not show that changing or removing the marker would cause a change in the condition, and other biological factors may explain the relationship.

Answer

Among adult patients represented by the sampling frame, the genetic marker is associated with higher prevalence of the condition. The observational study does not establish a cause-and-effect relationship.

54677712

A retailer randomly samples customers who have chosen English as their communication language and randomly assigns two versions of a payment reminder. Version B increases on-time payment. State the strongest causal and population conclusion.

Hints

- Use treatment assignment to decide whether causation is supported. - Define the population from the exact frame used for random selection. - Identify customers who were excluded before sampling began.

Solution

1. Random assignment supports a causal conclusion that Version B increases on-time payment. 2. Random selection supports generalization to customers in the English-language sampling frame. 3. Customers using other communication languages had no chance to be selected. 4. Therefore, the result should not automatically be generalized to the retailer's entire customer population.

Answer

Version B causes a higher on-time payment rate among customers represented by the English-language sampling frame. The result does not automatically generalize to customers who use other communication languages.

54678212

A company takes a simple random sample of employees and randomly assigns two evacuation-instruction formats. Format B reduces evacuation time in a computer simulation. State the strongest conclusion and explain the setting limitation.

Hints

- Tie the causal statement to the environment in which the response was measured. - Use random selection to identify the employee population represented. - Distinguish simulated performance from real-world behavior under stress.

Solution

1. Random assignment supports a causal conclusion about performance in the computer simulation. 2. Random selection supports generalization to the employee population represented by the sampling frame. 3. The measured response is simulated evacuation time, not behavior during an actual emergency. 4. Therefore, Format B can be said to reduce simulated evacuation time for that employee population, but the study does not establish the same effect in a real emergency.

Answer

Format B causes shorter evacuation time in the computer simulation for employees represented by the random sample. The result does not by itself establish that Format B would shorten evacuation time during an actual emergency.

54679212

A polling firm takes a simple random sample of voters and randomly assigns two descriptions of a proposed bond measure. One description increases the proportion who say they intend to vote for the measure. State the strongest conclusion and explain why actual voting behavior is outside the study's scope.

Hints

- Tie the causal statement to the exact survey response. - Use the random sample to identify the voter population represented. - Separate what respondents say they plan to do from what they later do.

Solution

1. Random assignment supports a causal conclusion that the description changes stated voting intention. 2. Random selection supports generalization to the voter population represented by the sampling frame. 3. The measured response is stated intention at the time of the survey. 4. The study does not establish that the wording changes actual votes cast later because actual voting behavior was not measured.

Answer

For voters represented by the random sample, the description causes a change in stated voting intention. The study does not show that it changes actual votes because voting behavior was not measured.

54681112

A seed company randomly selects \(240\) packets of one tomato cultivar from its current inventory. The packets are randomly assigned to receive either a new protective coating or the standard coating. Germination is measured under the same greenhouse conditions. State the strongest justified conclusion if the new coating produces a higher germination rate.

Hints

- Separate what random selection permits from what random assignment permits. - Identify exactly which packets were eligible to enter the study. - Notice the cultivar and environmental conditions that were held fixed.

Solution

1. Random assignment supports a cause-and-effect conclusion about the coating. 2. Random selection from the current inventory supports generalization to packets of this cultivar in that inventory. 3. The study does not justify generalization to other cultivars or substantially different growing conditions.

Answer

The new coating caused a higher germination rate for packets of this tomato cultivar in the company’s current inventory under the tested greenhouse conditions. The result cannot automatically be generalized to other cultivars or growing conditions.

54681212

An airport analyzes every medical-response call handled at its terminals during 2025. Calls with more response staff on duty tended to have shorter response times. What can the airport conclude, and what can it not conclude, from this study?

Hints

- Decide whether the study used a sample or included the entire stated group. - Ask whether the explanatory condition was assigned by chance. - Keep the conclusion within the location and time period actually observed.

Solution

1. Because every 2025 call at the airport was included, the observed association describes that finite set of calls without sampling uncertainty. 2. Staffing was not randomly assigned, so other factors such as crowd size or incident severity may be related to both staffing and response time. 3. The study does not establish causation and does not automatically generalize to other airports or years.

Answer

For this airport’s 2025 calls, higher staffing was associated with shorter response times. The study cannot show that higher staffing caused the shorter times, and it does not automatically support conclusions about other airports or years.

54682112

An electric utility takes an SRS of \(500\) customer homes that have smart thermostats. During July 2026, homes with lower daytime thermostat settings tend to use more electricity. State the strongest justified conclusion and two important limits.

Hints

- Identify the exact sampling frame. - Decide whether the thermostat setting was imposed or merely observed. - Keep the conclusion within the technology and time period represented in the data.

Solution

1. Random selection supports generalization to the utility’s customer homes with smart thermostats. 2. Thermostat settings were observed rather than randomly assigned, so the study supports association but not causation. 3. The conclusion does not automatically extend to homes without smart thermostats or to seasons other than July 2026.

Answer

Among the utility’s customer homes with smart thermostats, lower daytime thermostat settings were associated with greater electricity use during July 2026. The study does not establish causation and does not automatically apply to homes without smart thermostats or to other seasons.

54682612

A state agency takes an SRS of \(90\) public swimming pools. During one summer, pools with more lifeguards per \(100\) swimmers tend to report more rescues per \(1000\) swimmers. What scope of inference is justified, and why would a causal conclusion be especially misleading?

Hints

- Separate the role of random selection from the absence of random assignment. - Look for pool characteristics that could affect both staffing and rescues. - Avoid interpreting the direction of an association as the direction of a treatment effect.

Solution

1. Random selection supports generalizing the observed association to public swimming pools in the state during the summer studied. 2. Lifeguard staffing was not randomly assigned, so the study does not support causation. 3. Pools with stronger currents, larger crowds, or higher-risk activities may both employ more lifeguards and require more rescues, reversing the naive causal interpretation.

Answer

The association can be generalized to the state’s public swimming pools during the summer studied. It does not show that adding lifeguards causes more rescues, because higher-risk pools may both schedule more lifeguards and have more rescues.

54683112

A retailer takes an SRS of \(80\) pages from its current website and randomly assigns each page to use either the current image format or a new compressed format. Under a standardized network test, the new format reduces mean page-load time. Which causal conclusion is justified, and which tempting business conclusion is not justified?

Hints

- Identify the response variable actually recorded in the experiment. - Use the two kinds of randomization to determine population and causation. - Do not replace the measured technical outcome with an unmeasured customer outcome.

Solution

1. Random selection supports generalization to the retailer’s current website pages under the standardized network test conditions used in the study. 2. Random assignment supports the conclusion that the new format caused the reduction in page-load time. 3. Customer behavior was not measured, so the experiment does not show that the new format increases purchases, satisfaction, or retention.

Answer

For the retailer’s current website pages under the standardized network test conditions used in the study, the new format caused faster page loads. The study does not show that the format increases purchases, customer satisfaction, or retention.

54683212

A city has more eligible applicants for a housing-voucher program than available vouchers, so it awards vouchers by lottery. Researchers compare one-year housing stability for lottery winners and nonwinners who entered the lottery. Winners have greater housing stability. State the strongest justified conclusion and its population limit.

Hints

- Decide whether chance determined who received the program opportunity. - Identify the group whose members could have been assigned either outcome by the lottery. - Distinguish lottery entrants from the broader set of all eligible households.

Solution

1. The lottery assigns the opportunity to receive a voucher by chance, making the winner and nonwinner groups comparable for causal inference. 2. The result supports a causal conclusion about being offered a voucher among people who entered this lottery. 3. The applicants were not randomly selected from all eligible households, so the result does not automatically generalize to eligible households that did not apply or to other cities and program designs.

Answer

For people who entered this city’s lottery, being offered a housing voucher caused greater one-year housing stability. The result does not automatically generalize to nonapplicants, other cities, or different voucher programs.

54661812

Volunteers are randomly assigned to receive either a mindfulness app or no app. The response is self-reported stress after \(4\) weeks. Explain exactly what causal conclusion is supported and what limitation remains because of the response measure.

Hints

- State the outcome exactly as it was measured. - Use random assignment to decide whether causation is supported. - Keep measurement limitations separate from population limitations.

Solution

1. Random assignment supports a causal conclusion about the effect of app assignment on self-reported stress for the participants. 2. The response is self-reported, so reporting behavior may not equal physiological stress. 3. The study should claim an effect on reported stress, not automatically on every objective measure of stress. 4. Because the participants were volunteers rather than a random sample, statistical generalization to all adults is not justified.

Answer

The app caused a difference in self-reported stress among the participants. The study does not necessarily show the same effect on objective stress measures and should not be statistically generalized to all adults.

54669812

A community clinic recruits volunteer patients who have missed appointments. The patients are randomly assigned either to be offered a free transit pass or to receive the clinic's usual reminder. Some patients offered a pass never use it. The pass-offer group misses fewer appointments. What causal conclusion is justified, and what causal conclusion is not justified?

Hints

- Distinguish the condition assigned by the researchers from the behavior chosen by participants. - Base a causal statement on the randomized treatment, not on a later self-selected action. - Keep the population conclusion limited by how participants entered the study.

Solution

1. Random assignment supports a causal conclusion about the treatment actually assigned: being offered a free transit pass. 2. Because some assigned patients did not use the pass, pass use itself was not randomly assigned. 3. The study supports that offering a pass caused a reduction in missed appointments among the participants. 4. It does not by itself establish that actually using the pass or riding public transit caused the reduction, and volunteer recruitment does not support statistical generalization beyond the participants.

Answer

The study supports that offering a free transit pass caused fewer missed appointments among the participants. It does not establish that actually using the pass or riding transit caused the reduction, and it should not be statistically generalized beyond the participants.

54670312

Researchers take a simple random sample of juvenile trout from one lake and randomly assign the fish to two laboratory water-temperature conditions. Fish in the warmer condition gain less mass over \(30\,\text{days}\). State the strongest conclusion and identify two limits on its scope.

Hints

- Use random selection and random assignment for different parts of the conclusion. - Keep the response tied to the measured duration. - Note characteristics of the setting and population that were not varied or sampled.

Solution

1. Random assignment supports a causal conclusion that the tested warmer temperature reduces mean \(30\)-day mass gain. 2. Random selection supports generalization to juvenile trout from the sampled lake. 3. The conclusion is limited to the two tested temperature conditions and the \(30\)-day response period. 4. The experiment does not automatically establish the same effect for other lakes, adult trout, or natural lake conditions that differ from the laboratory.

Answer

For juvenile trout from this lake under the tested laboratory conditions, the warmer temperature causes lower mean mass gain over \(30\,\text{days}\). The result is limited to the tested temperatures and time period and should not automatically be generalized to other trout populations or field conditions.

54672312

Volunteers are randomly assigned to receive either a low dose or a high dose of a caffeine-free alertness supplement. The high-dose group has a larger mean improvement on a reaction-time task. There is no placebo or no-treatment group. State what causal conclusion is supported and what conclusion is not supported.

Hints

- Identify exactly which treatment conditions were randomly compared. - Restrict the causal statement to contrasts that the design actually contains. - Notice the comparison condition that is absent.

Solution

1. Random assignment supports a causal comparison between the two tested doses among the participants. 2. The study supports that the high dose causes a larger mean improvement than the low dose among those participants. 3. Because no group received placebo or no treatment, the study cannot determine whether either dose improves reaction time compared with receiving no supplement. 4. Volunteer recruitment prevents statistical generalization beyond the participants.

Answer

The high dose causes a larger mean improvement than the low dose among the participants. The study does not show that either dose is better than no supplement because no placebo or no-treatment group was included, and it should not be statistically generalized beyond the participants.

54673312

Researchers take a simple random sample of counties and find that counties with more public park acreage per resident tend to have lower adult obesity rates. State the county-level inference that is supported and explain why an individual-level conclusion is not supported.

Hints

- Identify the observational unit represented by each data point. - Keep the conclusion at the same level as the measured variables. - Ask whether any individual person's exposure and outcome were paired in the data.

Solution

1. Random selection of counties supports generalizing the observed county-level association to counties in the population represented by the sample. 2. The variables are county averages or rates, so the observational units are counties. 3. The study does not link individual residents' park access with their individual obesity status. 4. Therefore, it cannot conclude that a particular person with greater park access is less likely to have obesity, and it does not establish causation.

Answer

The study supports a population-level association among counties: counties with more park acreage per resident tend to have lower adult obesity rates. It does not support an individual-level claim about residents, and it does not establish that parks cause lower obesity rates.

54674312

A city randomly selects apartment buildings and randomly assigns each selected building either to receive a building-wide composting program or to remain under the usual waste system. Compost participation is measured for residents. State the strongest causal and population conclusion, making clear the level of treatment assignment.

Hints

- Identify the smallest unit that receives its own treatment assignment. - Use the building-selection process to set the population scope. - Phrase the causal conclusion at the same level as the randomized treatment.

Solution

1. Buildings are the experimental units because the composting program is assigned to whole buildings. 2. Random assignment supports a causal conclusion about offering the building-wide program. 3. Random selection of buildings supports generalization to apartment buildings in the city represented by the sampling frame. 4. The conclusion concerns the effect of a building-level program on resident participation, not separate independent treatment assignments to individual residents.

Answer

For apartment buildings in the city's sampling frame, assigning a building-wide composting program causes a change in resident compost participation. The treatment effect is a building-level program effect, not an independently randomized individual-resident effect.

54675712

A university randomly selects students from the full enrollment roster for an experiment, but only selected students who consent participate. The participants are then randomly assigned to two study tools. Tool A improves quiz scores. State the strongest justified scope of inference.

Hints

- Follow the sample from initial selection through actual participation. - Identify the stage at which self-selection enters. - Use random assignment for causation but use the final participating group for population scope.

Solution

1. Random assignment supports a causal conclusion among the students who participated. 2. Although the invitation list was randomly selected, participation depended on consent. 3. If consenters differ from nonconsenters in ways related to the response, the participating group is not a random sample of all students. 4. The result supports that Tool A causes higher quiz scores for the participating students, but it does not support statistical generalization to the full university enrollment.

Answer

Tool A causes higher quiz scores among the students who participated. Random assignment supports causation, but voluntary consent prevents statistical generalization to all university students.

54676212

Researchers recruit identical-twin pairs from a volunteer twin registry. Within each pair, one twin is randomly assigned a high-fiber diet and the other a usual diet. The high-fiber diet lowers mean cholesterol after six weeks. State the strongest causal and population conclusions.

Hints

- Use within-pair random assignment to decide whether causation is supported. - Identify what the pairing controls. - Use the recruitment method, not the assignment method, to set the population scope.

Solution

1. Random assignment within twin pairs supports a causal conclusion that the high-fiber diet lowers mean six-week cholesterol relative to the usual diet for the participating twins. 2. Matching twins controls genetic and many shared-background differences. 3. The pairs volunteered through a specialized registry rather than being randomly selected from all adults. 4. The result does not support statistical generalization beyond the participating twins.

Answer

The high-fiber diet causes lower mean cholesterol after six weeks for the participating twins. The matched-pairs randomization supports causation, but volunteer recruitment from a twin registry prevents statistical generalization to all adults.

54676712

A hospital reviews records for all patients who survived at least \(30\,\text{days}\) after a major procedure. Among these survivors, patients who began rehabilitation earlier had shorter hospital stays. State the scope of inference and explain why the study cannot address \(30\)-day survival.

Hints

- Identify the condition required for a patient to enter the dataset. - Keep the conclusion within the group satisfying that condition. - Ask whether the excluded patients are necessary for studying the survival outcome.

Solution

1. The dataset is restricted to patients who survived at least \(30\,\text{days}\), so conclusions apply only to that survivor population. 2. Rehabilitation timing was observed rather than randomly assigned, so the study supports an association, not causation. 3. Patients who died within \(30\,\text{days}\) are excluded by design. 4. Because the outcome used to define inclusion removes all nonsurvivors, the study cannot estimate or compare \(30\)-day survival for rehabilitation groups.

Answer

Among \(30\)-day survivors, earlier rehabilitation is associated with shorter hospital stays. The study does not establish causation and cannot draw conclusions about \(30\)-day survival because nonsurvivors were excluded.

54678712

A retailer takes a simple random sample of store-days from its October–December 2026 schedule and randomly assigns each selected store-day either to use a checkout promotion or not use it. The promotion increases mean daily sales. State the strongest conclusion and identify the experimental unit.

Hints

- Identify the smallest unit that receives its own promotion assignment. - Use random assignment for the causal statement. - Use the sampling frame to determine the population of units represented.

Solution

1. The experimental unit is a store-day because the promotion is assigned separately to each selected store on a particular day. 2. Random assignment supports a causal conclusion that the promotion increases mean daily sales. 3. Random selection of store-days supports generalization to the October–December 2026 population of store-days represented by the schedule. 4. The study does not provide independently randomized treatment effects for individual shoppers.

Answer

The experimental unit is a store-day. For store-days in the October–December 2026 schedule, using the checkout promotion causes an increase in mean daily sales. The conclusion is at the store-day level, not an independently randomized shopper-level effect.

54679112

Researchers use observational records to match people who chose a meal-delivery service with nonusers of similar age, income, and household size. Service users spend less time cooking. Does the matching support a causal conclusion? State the strongest inference.

Hints

- Distinguish making groups similar from assigning exposure by chance. - Identify variables that may not have been included in the match. - Phrase the conclusion as an association when self-selection remains.

Solution

1. Matching can make the two groups more similar on the variables used for matching. 2. Meal-delivery use was still self-selected rather than randomly assigned. 3. Unmeasured differences, such as work schedule or interest in cooking, may remain confounded with service use. 4. The study supports an association between service use and less cooking time among the matched people, but not a causal effect.

Answer

Matching does not create random assignment. The study supports an association between meal-delivery use and less cooking time among the matched people, but it does not establish that the service caused the reduction.

54679612

A national running organization takes a simple random sample of adult members and randomly assigns two hydration plans. Plan B improves mean race time overall. May the researchers conclude that Plan B improves race time for every age group and for both sexes? Explain.

Hints

- Distinguish an overall average effect from effects within subgroups. - Ask whether the study reports separate randomized comparisons for the named groups. - Keep the conclusion at the level directly supported by the analysis.

Solution

1. Random selection and random assignment support a population-level causal conclusion about the average effect for adult members represented by the sample. 2. An overall mean effect does not show that the effect has the same size or direction in every subgroup. 3. Subgroup conclusions require adequate representation and a planned analysis within the relevant age and sex groups. 4. The supported conclusion is an average causal effect for the full member population, not a guaranteed effect for each subgroup or individual.

Answer

The study supports that Plan B improves mean race time on average for the represented adult-member population. It does not prove the same effect for every age group, for both sexes separately, or for every individual without subgroup evidence.

54671812

A company takes a simple random sample of employees and randomly assigns them to a wellness program or a control group. Before the final measurement, \(35\%\) of the wellness group and \(5\%\) of the control group drop out. The analysis uses only employees who finish. Explain how the unequal dropout affects the scope of inference.

Hints

- Compare the proportions of missing outcomes across the two assigned groups. - Ask whether the people who remain are still likely to be comparable. - Distinguish the originally assigned sample from the smaller group included in the final analysis.

Solution

1. The original random selection and random assignment would support population-level causal inference if outcome data were retained comparably across groups. 2. Large differential dropout can make the remaining treatment and control groups systematically different. 3. A comparison of completers may therefore reflect both the treatment and differences in who remained. 4. The clean causal conclusion for all sampled employees, and its generalization to all employees, is weakened unless the missing outcomes are addressed appropriately.

Answer

Differential attrition can destroy the comparability created by random assignment among the analyzed completers. A complete-case comparison may not support a causal conclusion for all sampled employees or a generalization to all employees without addressing the missing outcomes.

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