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Bias in sampling

Learning goals

  • Identifies sources of selection, undercoverage, nonresponse, and voluntary-response bias.
  • Explains how bias can systematically distort estimates.
  • Distinguishes bias from random sampling variability.
  • Proposes design changes that reduce likely bias.

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Bias in sampling 1
At a crowded festival, an interviewer surveys the nearest person whenever a previous interview ends. Identify the sampling method and explain why it may be biased.

Hints

- Ask whether chance determines who is selected. - Identify which visitors are easiest for the interviewer to reach. - Explain why accessibility could be related to visitor characteristics.

Solution

1. The interviewer chooses whoever is easiest to reach. 2. This is convenience sampling, not random sampling. 3. People standing near the interview location or moving slowly are more likely to be included. 4. Those people may differ from the full festival population.

Answer

It is a convenience sample. Selection depends on proximity and timing, so some festival visitors are much more likely to be included than others.
Bias in sampling 2
Classify the main problem in each survey as nonresponse or voluntary response. a) A county randomly selects \(300\) residents and mails them a survey. Ninety selected residents never return it. b) A radio station posts a poll on its website and invites any visitor to answer.

Hints

- For each case, ask whether people were selected first and then failed to answer. - Contrast that with a survey in which people choose for themselves whether to join the sample.

Solution

1. In a), the residents were selected for the sample but some did not provide data. That is nonresponse. 2. In b), people decide for themselves whether to enter the sample. That is voluntary response.

Answer

a) Nonresponse. b) Voluntary response.
Bias in sampling 3
A county wants to survey all adult residents about housing costs. It draws addresses only from its list of single-family houses, leaving out apartment buildings. What sampling problem does this cause?

Hints

- Compare all adult residents with the addresses on the list. - Can someone in an apartment be selected? - What do we call it when a population group is left out of the list?

Solution

1. Adults who live in apartments belong to the target population. 2. Apartment addresses do not appear on the selection list. 3. This is undercoverage because a part of the population cannot be selected.

Answer

Undercoverage: adults in apartments are missing from the sampling frame.
Bias in sampling 4
A delivery center has day, evening, and overnight workers. A manager wants a random sample of all workers. Should the manager choose names from the day-shift list or from the complete employee roster? Explain.

Hints

- Does the study concern one shift or all shifts? - Which of the two lists includes everyone in the target population? - Who would be missing from the smaller list?

Solution

1. The intended population includes workers on all three shifts. 2. The complete roster gives every worker a chance to be selected. 3. A day-shift-only list would cause undercoverage of evening and overnight workers.

Answer

Use the complete employee roster. A day-shift-only list would leave out evening and overnight workers.
Bias in sampling 5
A county randomly selects \(100\) voters to answer a survey. It contacts all \(100\), but \(24\) decline to answer. Is the main problem undercoverage or nonresponse? Why?

Hints

- Were the missing voters eligible for selection? - Did their names appear in the selected group? - Which term describes selected people who do not reply?

Solution

1. The \(24\) voters were selected from the sampling frame. 2. They did not provide answers after they were contacted. 3. This is nonresponse rather than undercoverage.

Answer

Nonresponse. The \(24\) voters were selected but did not answer the survey.
Bias in sampling 6
A local news website asks readers to click a link if they want to answer a poll about a proposed skate park. No readers are randomly invited. What sampling problem is most likely?

Hints

- Who chooses who enters the survey? - Does every eligible resident get selected by chance? - Might people who care a lot be more likely to click?

Solution

1. Visitors decide for themselves whether to enter the poll. 2. People with strong opinions may be more likely to participate. 3. This is voluntary-response bias.

Answer

Voluntary-response bias, because readers choose for themselves whether to take part.
Bias in sampling 7
Two separate simple random samples of \(20\) students from the same school give different counts of students who ride the bus: \(8\) in one sample and \(11\) in the other. Does this difference by itself prove sampling bias? Explain.

Hints

- Were the students selected in the same random way? - Would every random sample necessarily include the same people? - Separate chance differences from a flawed selection method.

Solution

1. Random samples can contain different people. 2. Different counts can occur through chance variation even when the selection method is fair. 3. The two counts alone do not show a systematic sampling error.

Answer

No. Different random samples can give different results by chance; this is sampling variability, not proof of bias.
Bias in sampling 8
A survey asks, “Don't you agree that the town's wonderful new playground deserves more funding?” Is the main risk sampling bias or response bias? Explain.

Hints

- Focus on how the question is worded. - Does the wording sound neutral? - Is the problem how people are chosen or how they might answer?

Solution

1. The question uses approving language about the playground and funding. 2. This wording may push respondents toward agreement regardless of how they were selected. 3. The problem is response bias from leading wording.

Answer

Response bias. The leading wording may influence how people answer.
Bias in sampling 9
A town survey asks, “Do you support the responsible plan to protect families by adding more streetlights?” Explain the likely source of bias and rewrite the item to reduce it.

Hints

- Identify words that praise one response or make the alternative sound undesirable. - Preserve the policy choice while removing emotional language. - Keep the revised response options balanced.

Solution

1. Words such as “responsible” and “protect families” favor one response. 2. This creates question wording response bias. 3. A neutral version asks directly about support without persuasive language.

Answer

The wording is leading and can create response bias toward support. A less biased item is: “Do you support or oppose the proposal to add more streetlights in the town?”
Bias in sampling 10
Students complete a school survey that asks them to report how many energy drinks they consumed during the previous week. Their names are printed at the top, and coaches can view the responses. Identify the likely bias and explain a plausible direction.

Hints

- Consider whether respondents have a reason to conceal the true value. - Identify who can connect answers to individuals. - Use the likely reporting behavior to determine the direction.

Solution

1. The sensitive behavior is self-reported without anonymity. 2. Students may report socially desirable answers because coaches can identify them. 3. This is response bias and will likely make reported consumption lower than actual consumption.

Answer

Response bias is likely. Because the survey is identifiable and coaches can see it, some students may underreport energy-drink use, making the estimated mean consumption too low.
Bias in sampling 11
Police officers conduct face-to-face interviews outside a station and ask residents whether they have ever ignored a minor traffic law. Identify the likely source of bias and describe how the interview setting could affect responses.

Hints

- Consider whether the respondent may feel judged by the interviewer. - Compare a truthful answer with a socially safer answer. - Use that pressure to determine a likely direction.

Solution

1. The question concerns behavior that respondents may not want to admit. 2. The presence of police officers can influence answers away from the truth. 3. This is response bias caused by the interviewer and social desirability. 4. Residents will likely underreport ignoring traffic laws.

Answer

Response bias is likely. Interviewing residents face-to-face with police officers may lead them to underreport behavior that violates traffic laws.
Bias in sampling 12
A survey asks adults, “Do you exercise regularly?” Explain why the wording can create response problems and rewrite the item so answers are more comparable.

Hints

- Identify the word that different respondents may define differently. - Add a clear time period. - Ask for a measurable quantity rather than a vague label.

Solution

1. The word “regularly” has no fixed frequency or duration. 2. Respondents may interpret it differently, creating measurement and response bias. 3. A better item defines the activity, time period, and quantity to report.

Answer

The term “regularly” is ambiguous. One improved item is: “During the past \(7\) days, on how many days did you do at least \(30\,\text{minutes}\) of moderate or vigorous physical activity?”
Bias in sampling 13
A customer-service survey asks, “How would you rate our outstanding support?” The response options are “Excellent,” “Very good,” and “Good.” Identify two wording or response-option problems and explain their likely effect.

Hints

- Examine both the question stem and the available choices. - Ask whether a dissatisfied respondent has an accurate option. - Determine which direction the wording encourages.

Solution

1. The word “outstanding” is leading and favors a positive response. 2. All response options are positive, so dissatisfied customers cannot answer accurately. 3. These features create response bias and will tend to make support ratings appear more favorable than they are.

Answer

The question is leading, and the response scale omits neutral and negative choices. Both problems will likely bias ratings upward.
Bias in sampling 14
A survey asks shoppers to report exactly how much they spent at restaurants during the past \(12\) months. What measurement problem is likely, and how could the survey reduce it?

Hints

- How likely is someone to remember every restaurant purchase in one year? - Could a memory error be too high or too low? - What information could respondents record instead of recalling from memory?

Solution

1. Remembering exact spending for an entire year is difficult, so respondents may make memory errors. 2. These errors can make answers inaccurate. They produce systematic response bias only if the errors tend to go in one direction. 3. Asking about a shorter period or using receipts or a spending diary would improve accuracy.

Answer

People may not remember their spending accurately. Ask about a shorter period or use receipts or a spending diary. Memory errors are not necessarily a bias in one direction.
Bias in sampling 15
A campus survey asks, “Are you satisfied with the dining hall's food quality and operating hours?” Explain why the item is problematic and rewrite it.

Hints

- Count the distinct topics joined in the question. - Consider a respondent who likes one feature but dislikes the other. - Separate the topics while keeping the response scales comparable.

Solution

1. The item asks about two distinct features in one question. 2. A respondent may have different opinions about food quality and hours. 3. One answer cannot reveal which feature caused the response. 4. Split the item into two neutrally worded questions.

Answer

The item is double-barreled. Use separate questions, such as “How satisfied are you with the dining hall's food quality?” and “How satisfied are you with the dining hall's operating hours?”
Bias in sampling 16
Immediately after a televised political debate, a network invites viewers to text one of two numbers to vote for the winner. Explain why the result should not be reported as the preference of all debate viewers.

Hints

- Identify who controls entry into the poll. - Consider which viewers have the strongest motivation to text. - Compare respondents with the full audience.

Solution

1. Viewers choose whether to participate. 2. Those with strong opinions, greater enthusiasm, or easier access to texting may be more likely to respond. 3. This is voluntary response bias. 4. The respondents are not a random sample of all viewers.

Answer

The text poll is a voluntary response sample. Highly motivated viewers are overrepresented, so the result cannot represent all debate viewers.
Bias in sampling 17
Cafeteria staff measure food waste while visibly standing next to the disposal bins with clipboards. Explain why the measured waste might differ from waste on ordinary days.

Hints

- Would every student act the same way with staff watching? - Could watching change the behavior being measured? - Does the problem tell you exactly how students will respond?

Solution

1. Students can tell that their behavior is being watched. 2. Some may change how much food they take or where they throw it away. 3. This is an observer effect, also called reactivity: measuring behavior changes the behavior itself. 4. The recorded amount may no longer represent food waste on an ordinary day. Its direction depends on how students respond.

Answer

Visible observation can change students' behavior. This observer effect may make the recorded food waste different from usual, but the direction is not certain from the setup.
Bias in sampling 18
A software company emails a satisfaction survey to every customer but analyzes only the customers who choose to respond. A manager calls the results a census because everyone received the invitation. Evaluate that claim and identify the primary missing-data problem.

Hints

- Distinguish inviting every population member from obtaining data from every population member. - Classify people who were contacted but supplied no response. - Ask when the missing responses would systematically affect the satisfaction estimate.

Solution

1. A census requires data from every member of the population, not merely an invitation sent to every member. 2. Many contacted customers provide no data, so the analyzed responses do not constitute a census. 3. The primary problem is nonresponse: population members were contacted but did not respond. 4. The results can be biased if responding customers differ systematically in satisfaction from nonresponding customers.

Answer

The results are not a census because data were not obtained from every customer. The primary problem is nonresponse, and the satisfaction estimate may be biased if respondents differ systematically from customers who did not answer.
Bias in sampling 19
Immediately after resolving a customer's complaint, the same service agent asks the customer to rate the agent's performance aloud. Explain the likely response bias and suggest a less biased procedure.

Hints

- Consider how the respondent may feel when the person being evaluated is present. - Ask which direction politeness pressure would move the rating. - Separate the evaluator from the response-collection process.

Solution

1. The customer may feel pressure to avoid criticizing the agent directly or may answer out of politeness or gratitude. 2. This social interaction can systematically inflate ratings. 3. The rating should be collected privately through an anonymous or confidential system after the interaction, without the agent seeing or recording the response.

Answer

The face-to-face request can create courtesy or social-desirability bias, likely pushing ratings upward. Collect the rating privately and confidentially through a separate system.
Bias in sampling 20
An online survey asks whether users want to renew a service. The option “Yes, renew automatically” is preselected, and users must click another option to change it. Explain the likely bias and suggest a correction.

Hints

- Consider what is recorded when a respondent takes no action. - Ask whether one answer requires less effort than the others. - Make every response require the same deliberate action.

Solution

1. A preselected default can influence respondents who overlook the setting or accept it with little consideration. 2. The procedure can systematically increase recorded support for automatic renewal. 3. Present all choices without a preselected answer and require an active selection before submission.

Answer

The default can bias responses toward automatic renewal. Remove the preselection and require respondents to choose among neutrally presented options.
Bias in sampling 21
A survey asks, “How strongly do you disagree that the emergency alerts are not difficult to understand?” Explain the likely source of response bias and rewrite the item so that agreement has a clear meaning.

Hints

- Rewrite the statement without interpreting the response choices first. - Check how many reversals a respondent must mentally process. - Aim for one direct statement whose agreement direction is obvious.

Solution

1. The question combines a negative response direction with a negative statement, making the intended meaning difficult to interpret. 2. Respondents may answer inconsistently because they misread which response represents clear alerts. 3. A clear revision is “The emergency alerts are easy to understand,” with response choices ranging from strongly disagree to strongly agree.

Answer

The double-negative wording can cause response bias through misunderstanding. A clear revision is: “The emergency alerts are easy to understand,” followed by a balanced agreement scale.
Bias in sampling 22
A health survey asks adults how many urgent-care visits they had during the past \(12\) months. Follow-up interviews show that some respondents include memorable visits that occurred \(13\) or \(14\) months ago. Name the data-collection problem and describe its likely effect on the estimated mean number of visits.

Hints

- Compare the stated reference period with the dates respondents actually include. - Decide whether the mistake adds observations or removes them. - Use that direction to judge the effect on the mean.

Solution

1. Respondents are moving events from outside the requested period into the period, a recall problem often called telescoping. 2. Extra visits are counted even though they occurred before the \(12\)-month window. 3. The estimated mean number of visits is therefore likely biased upward.

Answer

This is recall bias caused by telescoping. It will likely bias the estimated mean number of urgent-care visits upward.
Bias in sampling 23
A public pool draws visit records at random from the numbered log in the diagram. It wants to estimate the mean length of all summer visits. Suppose season-pass visits last longer on average than single-day-ticket visits. Which visits will the sample miss, and is the estimate likely too high or too low? Explain.
Figure for problem 563348

Hints

- Trace where the records for the draw come from. - Think about what happens when a kind of visit is recorded somewhere else. - How would the overall mean change if shorter visits were included?

Solution

1. Only the pass-scan log is numbered for the random draw. Visits recorded in the single-day ticket log cannot be selected. 2. This is undercoverage even though records are drawn at random from the numbered log. 3. Because the included season-pass visits last longer on average, the sample is likely to overestimate the mean visit length for all summer visits.

Answer

Single-day-ticket visits are missing. This is undercoverage, and the mean length is likely too high because the sample includes only the longer season-pass visits.
Bias in sampling 24
A county wants opinions from all adult residents. Its resident directory omits adults living in dorms. It randomly selects \(500\) named adults from that directory, but \(180\) selected people do not reply. Name the two different problems and state a suitable fix for each.

Hints

- Separate people who had no chance to be chosen from people chosen but silent. - How might the address list be improved? - How might the study reach the people who did not respond?

Solution

1. Missing dorm residents cause undercoverage. Add dorm residents to the sampling frame using a suitable listing method. 2. Selected residents who do not reply cause nonresponse. Follow up with those selected residents to encourage replies. 3. Fixing one problem does not automatically fix the other.

Answer

Undercoverage: include dorm residents in the selection list. Nonresponse: follow up with selected people who did not answer.
Bias in sampling 25
A transit survey asks passengers, “How badly has the unreliable bus service disrupted your life?” The agency wants a fair measure of service satisfaction. Rewrite the question to reduce response bias while keeping the same subject.

Hints

- Which words in the original question assume a negative experience? - Can a satisfied passenger answer naturally? - Give respondents balanced choices instead of steering them toward a complaint.

Solution

1. The original wording assumes that service is unreliable and causes serious disruption. 2. A neutral item can ask respondents to rate satisfaction on a balanced scale. 3. The proposed item should let passengers report positive or negative views.

Answer

One valid revision is: “Overall, how satisfied are you with the bus service: very satisfied, somewhat satisfied, neither satisfied nor dissatisfied, somewhat dissatisfied, or very dissatisfied?”
Bias in sampling 26
A water district randomly selects households and tracks the survey process in the diagram. What percentage of selected households did not respond, and what kind of problem might this create?
Figure for problem 563355

Hints

- Which branch contains selected households that did not reply? - What is the denominator for a nonresponse percentage? - Why might missing replies affect the survey result?

Solution

1. The diagram shows \(45\) nonresponding households among \(120\) selected households. 2. The nonresponse percentage is \(\frac{45}{120}\cdot100\%=37.5\%\). 3. If responders differ from nonresponders on the survey topic, nonresponse bias may result.

Answer

\(37.5\%\) did not respond. The study could have nonresponse bias if responders differ systematically from those who did not reply.
Bias in sampling 27
A school surveys students about after-school jobs. What was the response rate among seniors? Which grade makes up a smaller share of replies than of the students selected?
Figure for problem 563356

Hints

- Identify the bars for selected seniors and senior replies. - A response rate compares replies with invitations for the same group. - Compare the mix of replies with the mix of people originally selected.

Solution

1. Of \(50\) selected seniors, \(10\) responded, so the senior response rate is \(\frac{10}{50}\cdot100\%=20\%\). 2. Junior respondents number \(30\) while senior respondents number only \(10\). 3. Seniors are less represented among completed responses than in the equally split selected sample.

Answer

Senior response rate: \(20\%\). Seniors are underrepresented among the completed responses.
Bias in sampling 28
A transit agency posts a survey link only on its social media account and asks riders to rate bus reliability. Identify the main potential sources of sampling bias and explain how they could affect the results.

Hints

- Ask who has a realistic chance to see the survey. - Ask who chooses whether to participate. - Do not claim a direction unless the scenario supports one.

Solution

1. Riders who follow the agency's social media account are more likely to be reached, creating undercoverage of other riders. 2. Participation is voluntary, so riders with unusually strong opinions may be more likely to respond. 3. Either effect can make the respondents unrepresentative of all riders; the direction of the bias cannot be determined from the information given.

Answer

Possible undercoverage and voluntary response bias. Riders not following the account are less likely to be included, and people with strong opinions may be more likely to respond. The direction of the resulting bias is not known.
Bias in sampling 29
A county mails a health survey to a simple random sample of residents. Only about one-fourth return it. Explain the potential bias and identify a difference between respondents and nonrespondents that would matter for estimating the proportion who have a regular primary-care provider.

Hints

- Focus on people who were selected but did not provide data. - Ask what characteristic could affect both responding and the survey variable. - Explain the likely direction only after stating that relationship.

Solution

1. Failure to obtain responses from many selected residents creates potential nonresponse bias. 2. Bias occurs if response behavior is related to whether a resident has a regular primary-care provider. 3. For example, residents who regularly use health services may be more likely to return a health survey, which could make the estimated proportion too high.

Answer

There is potential nonresponse bias. If residents with a regular primary-care provider are more likely to return the survey, the estimated proportion with a provider will tend to be too high.
Bias in sampling 30
To estimate the proportion of county households that own their homes, a researcher uses a printed residential landline directory as the sampling frame. Households without a listed residential landline therefore have no chance to be selected. County records show that households without listed landlines have a lower homeownership rate than households with listed landlines. Identify the likely bias and explain the likely direction of the estimate.

Hints

- Compare the printed-directory sampling frame with the full population of county households. - Identify which households have no chance to be selected. - Use the stated homeownership-rate difference to determine whether omitting that group pushes the estimate up or down.

Solution

1. The target population is all county households, but the sampling frame contains only households with listed residential landlines. 2. Households without listed landlines are omitted, so the design has undercoverage. 3. The problem states that the omitted households have a lower homeownership rate than covered households. 4. The sample therefore overrepresents the higher-homeownership group, so the estimated county household homeownership proportion will tend to be too high.

Answer

Undercoverage bias is likely. Households without listed residential landlines cannot be selected, and the problem states that these omitted households have a lower homeownership rate. Therefore, the estimated proportion of county households that own their homes will tend to be biased upward.
Bias in sampling 31
A parks department estimates average daily trail use by counting visitors only from \(9\) a.m. to \(3\) p.m. on weekdays. Identify the sampling problem and explain why the estimate may not represent all trail users.

Hints

- Compare the stated target period with the times actually observed. - Identify which users cannot appear in the data. - State the direction conditionally unless the scenario guarantees it.

Solution

1. Evening and weekend visitors are excluded from the observation periods. 2. This creates undercoverage because many members of the population have no chance to be counted. 3. If use is heavier outside the selected times, the estimate of average daily use will be too low; the exact direction depends on the unobserved use pattern.

Answer

The plan has undercoverage because it omits evenings and weekends. It cannot represent all trail users and may underestimate daily use if substantial use occurs during the excluded periods.
Bias in sampling 32
A restaurant prints a survey code on receipts with the message, “Tell us what you really think and enter to win dinner for a year.” The manager uses the responses to estimate the mean satisfaction rating of all customers. Explain the potential bias.

Hints

- Identify who controls entry into the sample. - Think about which experiences create stronger motivation to respond. - Avoid assigning a direction when both unusually satisfied and dissatisfied customers may respond.

Solution

1. Customers decide for themselves whether to respond. 2. People with unusually positive or negative experiences may be more motivated to participate. 3. The prize may also attract customers whose response behavior differs from that of typical customers. 4. This voluntary response sample may not represent all customers, and the direction of bias is not determined.

Answer

The survey is subject to voluntary response bias because customers choose whether to participate. Respondents may have stronger opinions or greater interest in the prize than typical customers, so the mean rating may be biased in an unknown direction.
Bias in sampling 33
A school district surveys families about access to after-school programs, but the survey is available only in English. Identify the likely sampling problem and explain how it could affect the estimate of unmet need.

Hints

- Identify which families face a barrier to responding. - Ask whether response likelihood may be related to the survey outcome. - Use that relationship to describe a plausible direction.

Solution

1. Families who cannot comfortably complete an English survey are less likely to respond. 2. This creates potential nonresponse bias because language access is related to participation. 3. If families needing another language face greater barriers to after-school programs, the survey will tend to underestimate unmet need.

Answer

The English-only survey creates potential nonresponse bias because families needing another language are less likely to participate. If those families have less access to programs, the estimated unmet need will likely be too low.
Bias in sampling 34
A city sends a survey to a random sample of residents. After the first mailing, it contacts nonrespondents twice by different methods. Explain how follow-up can reduce nonresponse bias and why it does not guarantee an unbiased estimate.

Hints

- Focus on how the composition of respondents changes after follow-up. - Ask what happens if the hardest people to reach remain different. - Distinguish reducing one bias from eliminating every bias.

Solution

1. Follow-up increases the chance of obtaining data from people who did not answer initially. 2. This can make respondents more similar to the full selected sample. 3. Bias can remain if some people still do not respond and those people differ on the variable of interest. 4. Other biases, such as response bias, may also remain.

Answer

Follow-up can reduce nonresponse bias by bringing more initially missing people into the data set. It does not guarantee an unbiased estimate because remaining nonrespondents may still differ systematically from respondents, and other sources of bias may persist.
Bias in sampling 35
A teacher surveys students who are present on one Monday about the average number of school days missed because of illness. Explain why surveying only students present that day can bias the estimate and state the likely direction.

Hints

- Identify who has no chance to respond on the chosen day. - Connect the reason for exclusion to the variable being estimated. - Use the missing values to determine the direction.

Solution

1. Students absent on the survey day cannot be included. 2. Students who miss more school because of illness are more likely to be absent that day. 3. This undercoverage will tend to omit higher values of the variable. 4. The estimated mean number of illness-related absences will likely be too low.

Answer

The plan undercovers students absent on the survey day, especially students who tend to miss more school. The estimated mean number of illness-related absences will likely be biased downward.
Bias in sampling 36
A transportation survey is conducted only among riders entering the central train station from \(6{:}30\) to \(8{:}30\) a.m. The results are used to estimate how all city residents usually travel. Identify the main bias.

Hints

- Compare the sampled location and time with the entire target population. - Identify transportation groups that cannot be selected. - Determine which travel mode is overrepresented by design.

Solution

1. Only morning train riders at one station can enter the sample. 2. Residents who drive, walk, bike, work different hours, or use other stations are excluded. 3. This convenience sampling frame creates severe undercoverage. 4. Train use will likely be overestimated for all city residents.

Answer

The sample has undercoverage and convenience bias because it includes only morning riders at one train station. It will likely overestimate the proportion of city residents who usually travel by train.
Bias in sampling 37
Before asking residents whether they support a new flood-control fee, a survey shows several dramatic photographs of flood damage. Explain how this survey order can bias responses and propose a fairer procedure.

Hints

- Consider what respondents see immediately before the target question. - Identify the emotion or viewpoint that material encourages. - Redesign the sequence so neither response is favored.

Solution

1. The photographs may prime fear or concern immediately before the policy question. 2. This context can create response bias toward supporting the fee. 3. A fairer procedure presents neutral factual information or asks the support question without persuasive material, using the same neutral wording for all respondents.

Answer

The photographs can prime respondents and bias support upward. Ask the policy question with neutral wording and without emotionally persuasive images, or present balanced information in a standardized way.
Bias in sampling 38
A school board asks for public comments about a boundary change at an evening meeting and treats the speakers' opinions as representative of all district families. Identify the main sampling biases.

Hints

- Separate who can attend from who chooses to speak. - Identify groups that the time and setting may exclude. - Consider which opinions create the strongest motivation to participate.

Solution

1. Families who attend an evening meeting are a convenience group and may differ from families who cannot attend. 2. Only people who choose to speak provide opinions, creating voluntary response bias. 3. Strongly affected or strongly opinionated families may be overrepresented. 4. The comments cannot represent all district families.

Answer

The comments have convenience and voluntary response bias. Meeting attendees are not a random cross-section of district families, and speakers self-select, likely overrepresenting people with strong opinions.
Bias in sampling 39
A wellness survey asks employees to state their current body weight from memory. The analyst then rounds every reported value to the nearest \(10\,\text{lb}\) before calculating the mean. Which step can create systematic response bias, and which step mainly reduces precision without having a guaranteed direction of bias? If employees tend to understate their weight, what direction of bias would that create in the estimated mean?

Hints

- Separate the respondent's reporting behavior from the analyst's rounding rule. - Ask whether each process tends to push values consistently in one direction. - Give a direction for the mean only when the stated behavior supports one.

Solution

1. Reporting weight from memory can create response bias if employees systematically understate or overstate their current weight. 2. Rounding to the nearest \(10\,\text{lb}\) coarsens the measurements, but ordinary nearest-value rounding can move individual values either upward or downward. 3. Therefore, rounding alone has no guaranteed direction of bias. 4. If employees tend to understate their weight, the estimated mean weight will be biased downward.

Answer

Self-reporting from memory can create systematic response bias. Rounding to the nearest \(10\,\text{lb}\) mainly reduces precision and has no guaranteed bias direction by itself. If employees tend to understate their weight, the estimated mean is biased downward.
Bias in sampling 40
A health department wants to estimate the proportion of older county residents who use telehealth. It samples only from the county's online-services account list, which excludes many older residents without reliable internet access. County service records show that older residents without reliable internet access use telehealth less often than those with reliable internet access. Explain the likely bias and direction.

Hints

- Compare who appears on the sampling frame with the full population of older county residents. - Identify the group with no chance to be selected from that frame. - Use the stated telehealth-use difference to determine the direction of bias.

Solution

1. The target population is all older county residents, but the sampling frame is limited to residents on the online-services account list. 2. Many older residents without reliable internet access have no chance to be sampled, creating undercoverage. 3. The problem states that the undercovered group uses telehealth less often. 4. The frame therefore overrepresents the higher-use group, so the estimated telehealth-use proportion will tend to be too high.

Answer

The online-services sampling frame creates undercoverage of older residents without reliable internet access. Because the omitted group has the lower stated telehealth-use rate, the estimated proportion of older county residents who use telehealth will tend to be biased upward.
Bias in sampling 41
A utility company sends a conservation survey only through its mobile app and uses the responses to estimate the proportion of all customers who understand time-of-use pricing. The company defines “understands” as answering at least \(4\) of \(5\) basic pricing questions correctly. In a prior audit, \(74\%\) of app users met this criterion, compared with \(46\%\) of nonusers. Identify the likely bias and direction.

Hints

- Identify which customers have no opportunity to respond through the chosen survey channel. - Compare the stated understanding rates for included and omitted customers. - Decide whether overrepresenting the higher-rate group pushes the estimate up or down.

Solution

1. Customers who do not use the mobile app are excluded from the survey channel, creating undercoverage. 2. The prior audit shows that the undercovered nonusers have a lower rate of meeting the stated understanding criterion than app users. 3. The app-only sample therefore overrepresents customers with the higher understanding rate. 4. The estimated proportion of all customers who understand time-of-use pricing will tend to be too high.

Answer

The app-only survey creates undercoverage of customers who do not use the app. Because the omitted nonusers have the lower stated understanding rate, the estimate of the proportion of all customers who understand time-of-use pricing will tend to be biased upward.
Bias in sampling 42
A randomly selected employee survey is returned by most employees, but many respondents leave the salary question blank. Identify the missing-data problem and explain when it would bias the estimated mean salary.

Hints

- Notice that people returned the survey but skipped one item. - Ask whether missingness is related to the value being estimated. - Use a stated relationship to determine a possible direction.

Solution

1. The blank salary responses are item nonresponse. 2. Bias occurs if employees who omit salary differ systematically in salary from those who report it. 3. For example, if high-salary employees are more likely to omit the item, the reported mean salary will tend to be too low.

Answer

This is item nonresponse. The mean will be biased if willingness to report salary is related to actual salary; for example, greater nonresponse among high earners would bias the mean downward.
Bias in sampling 43
Several interviewers translate the same survey question into another language in different ways during live interviews. Explain the potential bias and how to reduce it.

Hints

- Ask whether every respondent hears the same meaning. - Consider how wording differences affect comparability. - Standardize both the translated item and its administration.

Solution

1. Respondents may receive questions with different meanings or tones. 2. Inconsistent wording can systematically influence responses. 3. This creates question wording response bias and reduces comparability. 4. Use a professionally translated, tested, standardized version read the same way to every respondent.

Answer

Inconsistent translation can create response bias because respondents are effectively asked different questions. Use one validated translation and standardized interviewer instructions.
Bias in sampling 44
A refrigerator manufacturer wants the proportion of its 2018 compressors that needed a major repair within their first \(5\) years. It surveys only owners still enrolled in the company's maintenance program. Company records show that compressors needing major repairs were much more likely to be removed from the program than compressors needing no major repair. Identify the sampling bias and its likely direction.

Hints

- Does the maintenance list include every compressor from 2018? - Which repair-history group is more often left off the list? - How would missing that group affect the reported fraction needing repair?

Solution

1. The maintenance list does not cover every compressor from the 2018 batch. 2. Compressors that needed major repairs are especially likely to be missing from the list. 3. The survey therefore tends to miss compressors with the outcome being counted, creating undercoverage. 4. The estimated five-year major-repair proportion is likely too low.

Answer

Undercoverage. Compressors needing major repairs are more likely to be absent from the sampling frame, so the estimated repair proportion is likely biased downward.
Bias in sampling 45
A phone survey asks people to pick their most important local issue from six choices. Every interviewer reads the choices in the same order. How could this cause response bias, and how could it be reduced?

Hints

- Might the placement of a choice matter when people hear a list once? - Is there enough information to tell whether early or late choices are favored? - How could interviewers vary position while keeping the six choices unchanged?

Solution

1. A choice's position can affect how easily it is noticed or remembered. 2. Reading the same order to everyone may make certain positions more likely to be chosen, although the favored position is not known here. 3. Rotate or randomize the order of the same choices across respondents.

Answer

A fixed order can favor choices in certain positions. Randomizing or rotating the answer order can reduce this order effect.
Bias in sampling 46
A neighborhood survey asks one adult in each sampled household to report how many hours every other household member exercised during the previous week. Identify a likely response problem and explain how it could affect the data.

Hints

- Identify who performs the behavior and who supplies the answer. - Ask whether the respondent can observe the full behavior accurately. - Consider a collection method that gets closer to the person or event being measured.

Solution

1. The respondent may not know the exercise time of every other household member. 2. The answers are proxy reports rather than measurements or self-reports from the people whose behavior is being recorded. 3. Guessing, incomplete observation, or socially desirable assumptions can make the reported values differ systematically from the true values. 4. Collecting responses directly from each household member or using activity records would reduce the problem.

Answer

The survey is vulnerable to proxy-response bias because one person may not accurately know other household members' exercise time. The reports may systematically overstate or understate actual exercise. Direct reports from each person or objective records would be preferable.
Bias in sampling 47
Before asking customers to estimate their checkout wait, a survey states, “Many shoppers wait about \(15\,\text{minutes}\). About how long did you wait?” Explain how the stated value could bias responses and rewrite the question.

Hints

- Consider whether information supplied before the question could influence a person's estimate. - Identify the exact event that should mark the beginning and end of the wait. - Remove information that suggests what a typical answer should be.

Solution

1. The stated \(15\)-minute value can act as an anchor, pulling estimates toward that value even when actual waits differed. 2. The wording may therefore create systematic response bias in the reported wait times. 3. A neutral version is: “About how many minutes did you wait from joining the checkout line until your transaction began?”

Answer

The \(15\)-minute statement can anchor respondents' estimates near \(15\,\text{minutes}\). A neutral item is: “About how many minutes did you wait from joining the checkout line until your transaction began?”
Bias in sampling 48
A survey asks, “Should the city keep the current recycling schedule? Yes or no.” Some residents have no opinion or want a different schedule that is not represented by either response. Explain the potential bias and improve the response options.

Hints

- Compare the available choices with the full range of reasonable opinions. - Ask what a respondent must do when no option fits. - Add choices without steering respondents toward one position.

Solution

1. The forced yes-or-no choices do not represent all plausible opinions. 2. Respondents who are undecided or prefer another schedule must choose an inaccurate answer or skip the item. 3. This can systematically distort the distribution of opinions. 4. The survey should include balanced options such as keep the current schedule, change the schedule, and no preference or unsure, with a follow-up for the preferred change if needed.

Answer

The limited response choices can create response bias by forcing some residents into an inaccurate category. Add balanced options such as “keep it,” “change it,” and “no preference or unsure,” with an optional follow-up about the desired change.
Bias in sampling 49
A survey about a proposed soda tax begins with a large logo and message from an organization campaigning for the tax, although the individual survey questions are neutrally worded. Explain how the survey introduction could still create response bias and suggest a correction.

Hints

- Consider information respondents see before the first question. - Ask whether that information signals a preferred answer. - Separate necessary study information from persuasive material.

Solution

1. The sponsor message reveals the preferred position before respondents answer. 2. Respondents may alter answers to agree with the sponsor, oppose it, or give what they think is socially expected. 3. This can systematically affect responses even when the question wording itself is neutral. 4. Use a neutral introduction that states the study purpose without advocacy branding, and disclose sponsorship separately after responses when ethically appropriate.

Answer

The advocacy message can prime respondents and influence answers toward or against the sponsor's position. Use a neutral introduction without persuasive branding or statements before the survey items.
Bias in sampling 50
An online course sends a satisfaction survey only to students who complete the final module. The provider uses the results to describe everyone who enrolled. Identify the sampling problem and explain a likely direction of bias.

Hints

- Compare the survey-eligible group with everyone named in the conclusion. - Consider why some students fail to reach the final module. - Decide how those missing students' likely opinions would affect the estimate.

Solution

1. Students who withdrew or stopped participating before the final module cannot be surveyed, so they are undercovered. 2. Completion is likely related to satisfaction and course success. 3. Completers may be more satisfied than noncompleters, so the estimated satisfaction of all enrollees is likely too high.

Answer

The survey undercovers students who did not complete the course. Because noncompleters may be less satisfied, using only completers will likely bias the estimated satisfaction of all enrollees upward.
Bias in sampling 51
A survey asks adults to report the number of minutes they exercised last week. The data contain unusually many responses at \(30\), \(60\), \(90\), and \(120\) minutes. Identify the likely response pattern and explain how it can affect the data.

Hints

- Look for a repeated numerical pattern in the reported values. - Consider how people answer when they do not remember an exact amount. - Think of a collection method that reduces reliance on long-term recall.

Solution

1. The concentration at convenient round numbers suggests heaping caused by recall and rounding. 2. Respondents may replace uncertain values with nearby multiples of \(30\) rather than report exact minutes. 3. The pattern reduces measurement precision and can distort the distribution, especially frequencies near the heaped values. 4. Shorter recall periods or activity logs can reduce the problem.

Answer

The data show heaping: respondents are likely rounding uncertain memories to convenient multiples of \(30\). This response error reduces precision and distorts the distribution. A shorter recall period or recorded activity log would help.
Bias in sampling 52
Before answering a survey item about support for a proposal, each respondent is shown the current percentage of earlier respondents who supported it. Explain how this display could bias later responses and suggest a correction.

Hints

- Ask whether every respondent receives the same information before answering. - Consider how knowledge of a majority position can change a person's response. - Remove information generated by earlier participants from the response process.

Solution

1. The displayed percentage gives respondents information about the apparent majority position. 2. Some respondents may conform to the majority or deliberately react against it, so later answers are influenced by earlier answers. 3. The responses are no longer collected under the same neutral conditions. 4. Hide interim results until data collection is complete and present the item identically to every respondent.

Answer

Showing interim results can create conformity or reactance bias because later respondents are influenced by earlier responses. Do not display results until all responses have been collected.
Bias in sampling 53
During the week after a major holiday, a survey asks shoppers, “How much do you spend in a typical week?” The researcher intends to estimate spending during that specific holiday week. Explain the mismatch and how it could bias responses.

Hints

- Compare the reference period in the question with the period named in the study goal. - Consider whether behavior during the special week differs from ordinary behavior. - Replace the vague time phrase with exact dates.

Solution

1. The phrase “typical week” asks respondents to average over ordinary weeks rather than report the specified holiday week. 2. Holiday spending may be systematically higher or otherwise different from ordinary spending. 3. Responses may therefore underestimate or misrepresent spending during the target week. 4. The item should name the exact dates and ask for spending during that period.

Answer

The question measures ordinary-week spending, not spending during the target holiday week. Because holiday spending may differ systematically, the estimate can be biased. Ask about the exact named dates instead.
Bias in sampling 54
A national news website invites any visitor to answer an online poll. The poll opens at \(8\) a.m. Eastern time and closes after the first \(2000\) replies. Most places in western time zones have not yet reached midmorning when it closes. Identify two sources of sampling bias and suggest changes.

Hints

- Who decides which website visitors respond? - Can people in all time zones visit the poll before its response cap is reached? - Consider one change to selection and a separate change to the closing rule.

Solution

1. Website visitors choose whether to take part, so this is voluntary-response sampling. 2. Early closure gives people in western time zones less opportunity to respond, especially if they visit later in their day. 3. A planned probability sample of the target population would address self-selection better, and a fixed response window covering all time zones would address the timing problem.

Answer

The poll has voluntary-response bias and a time-zone timing imbalance. Invite a random sample of the target population and keep responses open for a planned period that gives every time zone a fair chance.
Bias in sampling 55
A city survey asks residents to rate a new transit app using these choices: “terrible,” “poor,” “acceptable,” “good,” “very good,” and “excellent.” Explain how the response scale could bias the results, and rewrite the choices as a balanced five-point scale.

Hints

- Compare how many choices express approval with how many express disapproval. - Look for a neutral midpoint and matching categories on both sides of it. - Ask whether the wording gives every overall attitude an equally natural response.

Solution

1. The original scale has more favorable categories than unfavorable categories, which can make positive responses easier or more likely to select. 2. A balanced scale has matching positive and negative categories with a neutral midpoint. 3. One valid revision is “very dissatisfied,” “dissatisfied,” “neither satisfied nor dissatisfied,” “satisfied,” and “very satisfied.”

Answer

The original choices can create response bias because they contain more positive than negative options. A balanced revision is: “very dissatisfied,” “dissatisfied,” “neither satisfied nor dissatisfied,” “satisfied,” and “very satisfied.”
Bias in sampling 56
Researchers place electronic counters on hiking trails to estimate winter use. The counters are more likely to shut down on very cold days, and trail use is usually lower on those days. Explain how deleting all days with missing counts could bias the estimated mean number of hikers per winter day.

Hints

- Identify which days are most likely to be absent from the data. - Compare expected trail use on missing days with use on recorded days. - Decide which direction the remaining observations would pull the mean.

Solution

1. Missingness is related to temperature, and temperature is related to trail use. 2. The deleted days tend to be days with lower trail counts. 3. The remaining data overrepresent warmer, busier days, so the estimated winter daily mean is likely biased upward.

Answer

The estimate is likely biased upward because the missing days are disproportionately very cold days, when trail use tends to be lower.
Bias in sampling 57
In a school survey of \(1000\) students, only \(600\) answered a question about riding the bus to school. Among those who answered, \(180\) said they rode the bus. a) What percentage of students who answered take the bus? b) Can you find the percentage of bus riders among all \(1000\) students from this information alone? Explain. c) Under what assumption would the answer from part a) be a reasonable estimate for all students?

Hints

- Which students do the survey answers actually describe? - How many students have an unknown travel method? - Would the estimate change if the nonrespondents rode the bus at a different rate?

Solution

1. Among the \(600\) respondents, \(180\) ride the bus, so their rate is \(180/600=0.30=30\%\). 2. The travel method of the \(400\) students who did not answer is unknown, so the full-school percentage cannot be determined exactly. 3. If nonrespondents ride the bus at the same rate as respondents, \(30\%\) is a reasonable full-school estimate.

Answer

a) \(30\%\). b) No. We do not know how many of the \(400\) nonrespondents ride the bus. c) Assume the same bus-riding rate among respondents and nonrespondents.
Bias in sampling 58
A city wants the proportion of all adults who visit a gym weekly. It randomly surveys adults with listed landlines, leaving out adults with only mobile phones. An official says this must overestimate weekly gym visits. Explain why the direction of bias is not known. Give one possible pattern among excluded adults that would make the estimate too high and another that would make it too low.

Hints

- Which population group has no chance to appear in the sample? - Does the missing group have to share the same gym-going habits as the people on the list? - Test two opposite assumptions about the missing group's habits before claiming a direction.

Solution

1. Mobile-only adults cannot enter the sample, so there is undercoverage. 2. If mobile-only adults visit gyms less often than landline adults, the landline estimate tends to be too high. 3. If mobile-only adults visit gyms more often, the landline estimate tends to be too low. 4. Without information about the excluded adults, neither direction is justified.

Answer

Undercoverage alone does not fix the direction. If excluded mobile-only adults visit gyms less often, the estimate may be too high; if they visit more often, it may be too low.
Bias in sampling 59
An arts organization emails a survey to a random sample of former ticket buyers, but many older email addresses are no longer active. Explain whether the main concern is undercoverage, nonresponse, or both.

Hints

- Distinguish people absent from the sampling frame from people selected but missing a response. - Classify each failure at the point where it occurs. - Explain why either group could differ from the observed respondents.

Solution

1. If inactive addresses remain in the sampling frame and selected people cannot be reached, those selected units become nonrespondents. 2. If the frame itself omits former buyers without usable email addresses, those people are undercovered. 3. Both problems can occur, depending on how the frame and failed deliveries are handled.

Answer

Both may occur. Former buyers omitted from the email frame are undercovered, while selected buyers whose messages fail or who do not reply create nonresponse. Either can bias results if the affected buyers differ from respondents.
Bias in sampling 60
A city randomly selects households for a survey about emergency preparedness. When a selected household does not answer the door, the interviewer immediately surveys the nearest household instead. Explain why this substitution does not solve the nonresponse problem and may introduce additional bias.

Hints

- Track what happens to the originally selected household after it fails to respond. - Ask whether the replacement is chosen by chance from the full sampling frame. - Consider whether neighboring households may resemble one another in ways related to preparedness.

Solution

1. The selected nonresponding households are still missing, so any systematic difference between respondents and nonrespondents remains. 2. The replacement households are chosen by proximity rather than by the original random mechanism. 3. Nearby households may share housing type, income, or neighborhood conditions, so the substitutions can overrepresent characteristics of areas where interviewers already obtained responses.

Answer

The procedure leaves the original nonresponse bias unresolved because the selected households still provide no data. It also adds nonrandom selection: nearest households are convenience replacements and may be systematically similar to the responding neighborhood households.
Bias in sampling 61
A chamber of commerce randomly samples businesses from a directory that has not been updated in three years. Many sampled phone numbers belong to businesses that have closed. Explain the resulting data-collection problem and when it could bias an estimate of current businesses' hiring plans.

Hints

- Compare the directory with the population as it exists now. - Look for both ineligible entries and eligible units that may be absent. - Decide what relationship would make the frame problem affect the hiring estimate.

Solution

1. The outdated frame includes units that are no longer members of the current population, producing many ineligible contacts and missing responses. 2. The problem can also signal that newer businesses are absent from the frame, creating undercoverage of current businesses. 3. The estimate is biased if newly opened or surviving businesses have systematically different hiring plans from the businesses adequately represented by the old directory.

Answer

The outdated directory creates frame errors: closed businesses are included, and newer current businesses may be omitted. Bias results if the current businesses missing from or poorly represented in the frame have different hiring plans from those that can be contacted.
Bias in sampling 62
An interviewer visits sampled households and always asks the person who answers the door for that person's opinion about a city ordinance. The results are reported as opinions of all adults in the sampled households. Identify the selection problem within households and explain a likely source of bias.

Hints

- Separate how households are selected from how a person is selected inside each household. - Ask whether every eligible adult has the same opportunity to respond. - Consider characteristics associated with being home and answering the door.

Solution

1. The adult who answers the door is selected by availability rather than by a random mechanism within the household. 2. Adults who are home at the interview time may differ in age, work schedule, caregiving responsibilities, or opinions from other adults. 3. Therefore, the procedure can systematically underrepresent adults who are less likely to answer the door. 4. The interviewer should randomly select one eligible adult within each sampled household or collect responses from all eligible adults if the design permits.

Answer

The procedure uses nonrandom within-household selection. Adults who answer the door may differ from other adults in ways related to the ordinance, creating bias. Randomly select an eligible adult within each household instead.
Bias in sampling 63
A workplace survey measures morale using ten statements, all phrased so that agreeing indicates high morale. Explain how a tendency to agree with statements could bias the score and describe a design improvement.

Hints

- Consider a respondent who agrees with most statements automatically. - Ask what happens when every agreement receives a high-score interpretation. - Change the item set so the same response pattern does not always push the score one way.

Solution

1. Some respondents tend to agree with statements regardless of their exact content. 2. When every item is keyed in the same direction, this acquiescence tendency can systematically inflate morale scores. 3. The survey can include carefully written statements keyed in both directions, with scoring reversed where appropriate, while avoiding confusing double negatives. 4. Clear neutral wording and validation of the scale can further reduce the problem.

Answer

A general tendency to agree can inflate morale scores because all items point in the same direction. Use a balanced set of clearly worded positive and negative items and reverse-score the appropriate items.
Bias in sampling 64
A phone survey uses automatic speech recognition to record spoken answers. The software fails more often for some accents and marks those responses as missing. Explain the potential bias and suggest a correction.

Hints

- Identify whether recording failures occur equally across respondents. - Consider what other characteristics may be associated with the failure pattern. - Provide a response method that does not depend on the same recognition process.

Solution

1. Missingness depends on speech characteristics rather than occurring randomly. 2. Speakers whose accents are recognized less accurately are underrepresented in the recorded data. 3. If accent is related to geography, language background, or the survey variable, estimates can be systematically biased. 4. Use validated multilingual or accent-robust systems, provide keypad or human-assisted alternatives, and review recognition failure rates across groups.

Answer

The recognition system creates differential missingness and underrepresents speakers whose accents it handles poorly. Offer reliable alternative response modes and validate the system across the population before using the data.
Bias in sampling 65
A health survey interviews younger adults through an anonymous web form but interviews older adults by phone with a live interviewer. The groups report different rates of a sensitive behavior. Explain why survey mode is a possible source of bias.

Hints

- List what differs between the groups besides age. - Consider how privacy and interviewer presence affect sensitive answers. - Redesign the collection so mode does not vary only with age group.

Solution

1. Survey mode is completely linked to age group. 2. Anonymous web responses and live phone responses may produce different levels of privacy, social pressure, and willingness to disclose sensitive behavior. 3. The observed age-group difference may therefore reflect both true age differences and mode-related response bias. 4. Use the same mode across groups or randomly assign modes within each age group so mode effects can be separated from age effects.

Answer

Survey mode is confounded with age group. Live phone interviews may produce different disclosure than anonymous web forms, so the reported difference may partly be a mode effect. Use a common mode or randomize modes within age groups.

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