Potential Problems with Sampling
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AP Statistics › Potential Problems with Sampling
A town wants to estimate the proportion of all registered voters in the town who support a proposed bond measure. The town clerk takes the voter registration list, sorts it alphabetically by last name, and selects every 20th name starting with the first name on the list. The clerk assumes this produces a representative sample. Which issue most threatens the validity of this sampling method?
Nonresponse bias because selecting every 20th name guarantees refusals
Response bias because bond measures are too complex to ask about
Sampling variability because systematic sampling always has zero variability
Voluntary response bias because voters chose whether to be selected
Potential bias from a systematic sample if the ordering is related to support (for example, last name correlated with neighborhood or ethnicity)
Explanation
Potential bias in systematic sampling is the focus of this AP Statistics question. The clerk sorted voters alphabetically by last name and selected every 20th, assuming representativeness for support of a bond measure among all registered voters. This threatens validity if the ordering correlates with opinions, like last names linked to ethnic or neighborhood groups that differ in support. Voluntary response bias (choice B) is a distractor, as selection was systematic, not self-chosen. Mini-lesson: when diagnosing sampling issues, check for patterns in the list that systematic methods might exploit; random selection avoids such biases by equalizing chances.
A city wants to estimate the mean number of minutes commuters spend on public transit each weekday for all city residents who commute. Surveyors stand at one downtown subway station from 7:00–8:00 a.m. on a Tuesday and ask every 5th rider entering the station how long their commute is. The city reports the result as representing all commuters in the city. Which issue most threatens the validity of this sampling method?
Nonresponse bias because every 5th rider was required to answer
Voluntary response bias because only people with strong opinions participated
Simple random sampling because every commuter had an equal chance to be selected
Measurement error because commute times should have been recorded with a stopwatch
Convenience sampling that overrepresents commuters who use that station at that time
Explanation
In AP Statistics, this question assesses the ability to spot potential sampling issues like convenience sampling. The surveyors selected commuters at one specific subway station during a narrow morning window on a weekday, using a systematic approach of every 5th rider but limiting the frame to that location and time. This threatens validity because it overrepresents downtown subway users during rush hour, who may have different commute times than bus riders, evening commuters, or those using other stations. A distractor is voluntary response bias (choice D), which doesn't apply since participants were approached rather than self-selecting. A mini-lesson on diagnosing sampling problems: evaluate if the sampling process gives all population members an equal chance or if convenience leads to undercoverage of subgroups, as seen here where non-subway or off-peak commuters are excluded.
A principal wants to estimate the average number of hours of sleep per night for all students at the high school. She selects a sample by surveying students who arrive early to school to attend a 7:00 a.m. tutoring program, recording their reported sleep from the previous night. Which issue most threatens the validity of this sampling method?
Sampling variability because a sample mean is always different from the population mean
Measurement error because sleep must be measured with a device, not a survey
Response bias because students might exaggerate their sleep to impress the principal
Undercoverage because students who do not attend early tutoring are not represented
Nonresponse bias because some early-arriving students might skip the survey
Explanation
In AP Statistics, this question tests the ability to spot potential sampling issues, particularly when the sample doesn't cover the entire population of interest. The principal surveys only students arriving early for a 7:00 a.m. tutoring program, aiming to estimate average sleep for all high school students. This method introduces undercoverage because students not attending early tutoring—perhaps those who sleep later or have different schedules—are not included, potentially biasing the results toward students with specific habits. For instance, early risers might report more sleep, unrepresentative of the whole school. A distractor like nonresponse bias (choice A) might seem plausible, but the core problem is the incomplete coverage of the population, not just skipping the survey. A mini-lesson on diagnosing sampling problems: Evaluate if the sampling method systematically omits subgroups, and consider how that affects generalizability to the population parameter. Recognizing undercoverage promotes better sampling designs for accurate inferences.
A local news station wants to estimate the proportion of all adults in the county who support a proposed sales-tax increase. During the evening broadcast, the station asks viewers to text YES or NO, and it reports the results from the 8,500 texts received. Which issue most threatens the validity of the station’s conclusion?
Voluntary response bias because people with strong opinions are more likely to text
Random assignment bias because viewers were not randomly assigned to watch the broadcast
Confounding because tax support depends on income
Nonresponse bias because some viewers did not own phones capable of texting
Measurement error because YES/NO responses should be on a 1–5 scale
Explanation
This question tests recognition of voluntary response bias in media polls. The news station wants to estimate support among ALL county adults but relies on viewers who choose to text during the broadcast. This creates strong voluntary response bias because people with passionate opinions (either strongly for or against the tax) are much more motivated to take action and text their response. Additionally, the sample is limited to people watching that particular news broadcast who also have texting capability and choose to participate. Even with 8,500 responses, this self-selected sample likely overrepresents extreme views and underrepresents moderate or indifferent adults. Media call-in or text-in polls are classic examples of voluntary response bias - they measure the opinions of motivated responders, not the general population. To diagnose this issue, ask whether participation requires extra effort that might correlate with the variable being measured.
A county health department wants to estimate the proportion of all adults in the county who have received a flu vaccine this season. They draw a simple random sample from a list of adults who visited any county-run clinic in the past year and call those selected. The department reports the result as the countywide vaccination rate. Which issue most threatens the validity of this sampling plan?
Response bias because vaccination status should be measured by a blood test
Nonresponse bias because the department used phone calls instead of texts
Voluntary response bias because the sample was not randomly chosen
Undercoverage because adults who did not visit a county-run clinic are not in the sampling frame
Randomization error because a simple random sample cannot be used for proportions
Explanation
Identifying undercoverage as a sampling problem is key in this AP Statistics scenario. The health department sampled randomly from adults who visited county clinics in the past year, then called them to ask about flu vaccines, reporting results for all county adults. This method's validity is threatened because non-clinic visitors are completely excluded from the sampling frame, and they might have lower vaccination rates due to less health engagement. A distractor is voluntary response bias (choice C), but the sample was randomly chosen, not self-selected. A mini-lesson: to diagnose undercoverage, ensure the sampling frame covers the entire population; here, restricting to clinic visitors misses large segments, leading to biased estimates.
A university wants to estimate the proportion of all undergraduate students who are satisfied with campus dining. The university emails a survey link to 3,000 randomly selected undergraduates. After two reminder emails, only 620 students complete the survey. The university uses these 620 responses to estimate overall satisfaction. Which issue most threatens the validity of the estimate?
Voluntary response bias because the sample was drawn from a random list
Nonresponse bias because many selected students did not respond and may differ from responders
Undercoverage because students who eat off campus cannot be surveyed
Sampling variability because a sample size of 620 is always too small
Response bias because satisfaction cannot be measured with a survey
Explanation
This AP Statistics question focuses on potential problems with sampling, particularly nonresponse bias. The university randomly selected 3,000 undergraduates and emailed surveys, but only 620 responded despite reminders, and they used just those responses to estimate satisfaction for all undergrads. Validity is threatened because nonrespondents might differ systematically—perhaps less satisfied or busier students ignored the survey, biasing the results. Undercoverage (choice C) is a distractor, but the issue isn't the sampling frame excluding off-campus eaters; it's the low response rate. For diagnosing sampling problems, check response rates and consider if nonrespondents could have different views, as high nonresponse often indicates bias in who actually provides data.
A company wants to estimate the mean job satisfaction score (1–10) for all employees. The HR department selects a simple random sample of 200 employees and asks them to complete a satisfaction survey in a group meeting led by their direct managers, who can see who turns in each survey. Which issue most threatens the validity of the results?
Sampling bias because the sample size of 200 is too large
Nonresponse bias because a simple random sample guarantees everyone responds
Undercoverage because only employees with managers were surveyed
Response bias because employees may not answer honestly when managers can identify them
Voluntary response bias because employees chose whether to be in the sample
Explanation
This question in AP Statistics examines response bias as a potential sampling issue. The company took a simple random sample of 200 employees but conducted surveys in manager-led meetings where responses weren't anonymous, potentially causing employees to inflate satisfaction scores out of fear. Validity is threatened because the lack of privacy may lead to dishonest answers, not reflecting true job satisfaction across all employees. Undercoverage (choice B) distracts by misapplying the concept, as all employees were in the frame regardless of having managers. Diagnosing sampling problems involves checking not just selection but also how data is collected; here, the non-anonymous setting introduces response bias by influencing honesty.
A restaurant chain wants to estimate the proportion of all customers who would recommend the restaurant. Receipts include a QR code inviting customers to complete a short survey for a chance to win a $50 gift card. The chain summarizes the survey responses and reports them as representative of all customers. Which issue most threatens the validity of this approach?
Nonresponse bias because a random sample was selected but many refused
Undercoverage because every customer receives a receipt
Measurement error because recommendations should be measured by tracking repeat visits
Voluntary response bias because customers self-select into responding, possibly based on strong experiences
Sampling variability because incentives eliminate bias
Explanation
Voluntary response bias is the core sampling problem tested in this AP Statistics question. The restaurant invited all customers via receipt QR codes to take a survey for a gift card chance, then treated responses as representative of all customers' recommendation rates. This threatens validity because self-selecting participants, even with incentives, often have stronger opinions—dissatisfied customers might be more motivated to respond. Undercoverage (choice B) is a distractor since receipts reach everyone, but the issue is who chooses to participate. A mini-lesson on diagnosis: look for self-selection in sampling processes, as it biases results toward extremes, unlike random methods that aim for representativeness.
A gym wants to estimate the mean number of visits per month for all gym members. The manager surveys members who are present at the gym on Saturday afternoon and asks how many times they visited in the past month. The manager reports the sample mean as the average for all members. Which issue most threatens the validity of this conclusion?
Convenience sampling that likely overrepresents more frequent users who are at the gym on that day
Nonresponse bias because Saturday visitors are unlikely to answer questions
Voluntary response bias because the manager randomly selected members from a list
Undercoverage because only members with membership cards can be surveyed
Response bias because the manager should have asked for exact dates of visits
Explanation
Convenience sampling as a problem is central to this AP Statistics question. The gym manager surveyed only members present on a Saturday afternoon, using their reported visits to estimate the mean for all members. This method's validity is threatened because it overrepresents frequent or weekend users, who likely visit more often than average members. Voluntary response bias (choice C) distracts, but the manager approached people, not relying on self-selection. For diagnosing sampling problems, assess if accessibility drives selection; convenience often biases toward certain behaviors, as seen with gym attendance here.
A school district wants to estimate the proportion of all parents of students in the district who support switching to a year-round calendar. The district posts a link to an online poll on its homepage and social media accounts and leaves it open for 48 hours. A total of 1,842 responses are submitted, and the district reports the poll result as representing districtwide parent opinion. Which issue most threatens the validity of this sampling method?
Undercoverage because parents without reliable internet access are less likely to be included
Nonresponse bias because some selected parents refused to answer after being contacted
Voluntary response bias because the sample consists of people who chose to participate
Response bias because the question wording must have been leading
Randomization error because the district did not use a larger sample size
Explanation
This question tests the skill of identifying potential problems with sampling in AP Statistics, specifically recognizing voluntary response bias. The school district used an online poll accessible via their homepage and social media, allowing parents to self-select into the sample by choosing to participate. This method threatens validity because those with strong opinions on the year-round calendar are more likely to respond, potentially skewing results away from the true proportion among all parents. A common distractor here is undercoverage (choice A), which might seem plausible if focusing on internet access, but the primary issue is the self-selection inherent in voluntary response. To diagnose sampling problems, always compare the sampling method to the population of interest and check if certain groups are systematically over- or underrepresented due to how the sample is chosen. In this case, the lack of random selection means the sample isn't representative, leading to biased estimates.