AP Statistics Quiz: How Collected Data Tells The Truth

What this quiz covers

This quiz focuses on How Collected Data Tells The Truth, giving you a quick way to practice the rules, question types, and explanations that matter most for AP Statistics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. The conclusion is not valid because the sample is a convenience sample of gym-goers at a particular time and may not represent all adults in the city. (correct answer)
2. The conclusion is valid because 85 is a sufficiently large sample size for estimating a mean.
3. The conclusion is valid because the sample mean is greater than 7, so the population mean must be greater than 7.
4. The conclusion is not valid because the interviewers should have measured sleep in minutes, not hours.
5. The conclusion is valid because exercising in the morning causes people to sleep more, which supports the claim.

Explanation: This question examines how convenience sampling undermines the validity of generalizations to a larger population. The health department surveyed only people leaving a downtown gym on weekday mornings, creating a convenience sample that likely overrepresents health-conscious individuals who exercise regularly and may have different sleep patterns than the general adult population. People who go to the gym in the morning might prioritize sleep more or have schedules that allow for adequate rest. The sample mean of 7.4 hours cannot reliably estimate the mean for all city adults because the sampling method systematically excludes many groups (non-exercisers, people with different work schedules, etc.). A valid conclusion would require random sampling from all adults in the city, not just gym-goers.

Question 2

1. The conclusion is valid because random-digit dialing always produces a simple random sample of voters.
2. The conclusion is not valid because 520 is too small to estimate a proportion for an entire county.
3. The conclusion is not valid because limiting calls to landlines may underrepresent voters who use only cell phones, so the sample may be biased. (correct answer)
4. The conclusion is valid because the survey asked about approval, which is an objective fact.
5. The conclusion is valid because approval of the location causes people to keep landlines, making the estimate more accurate.

Explanation: This question illustrates coverage bias, where the sampling method systematically excludes certain population segments. By using random-digit dialing limited to landline phones, the election office excludes voters who rely exclusively on cell phones, a group that tends to be younger and may have different political views. This creates undercoverage of an important demographic, potentially biasing the approval estimate. While random-digit dialing of landlines was once considered good practice, changing communication patterns have made it problematic for representing entire populations. The 61% approval estimate may not accurately reflect all registered voters' opinions if cell-phone-only users have different views about the voting center location. Modern polling must include cell phones or use other methods to ensure all voter segments have a chance of selection.

Question 3

1. The conclusion is valid because selecting 8 schools at random guarantees that the parents surveyed at those schools form a random sample of all district parents.
2. The conclusion is not valid because surveying only PTA meeting attendees may overrepresent more involved parents, so the sample may not represent all parents in the district. (correct answer)
3. The conclusion is valid because cluster sampling always produces unbiased results, regardless of who responds within clusters.
4. The conclusion is not valid because the sample percentage would be valid only if exactly 32 schools were selected.
5. The conclusion is valid because requiring uniforms would cause parents to support uniforms, so the estimate must be correct.

Explanation: This question illustrates how cluster sampling can introduce bias when combined with convenience sampling within clusters. While the district appropriately randomly selected 8 schools (clusters) from 32, they then surveyed only parents attending PTA meetings at those schools. PTA meeting attendees likely overrepresent parents who are more involved in school activities, have strong opinions about school policies, and have schedules permitting meeting attendance. These parents may have different views on uniforms than less-involved parents or those unable to attend meetings. The 64% support estimate probably doesn't represent all district parents accurately. For valid conclusions, the district should have randomly sampled parents within each selected school rather than relying on PTA meeting attendance, which creates a biased sub-sample within each cluster.

Question 4

1. The conclusion is valid because weighing 60 fish is enough to estimate a mean for the entire lake.
2. The conclusion is not valid because the fish were caught at only two accessible shoreline locations and one time, so the sample may not represent all adult trout in the lake. (correct answer)
3. The conclusion is valid because using nets prevents any selection bias in which fish are caught.
4. The conclusion is not valid because fish weight is categorical, so a mean cannot be computed.
5. The conclusion is valid because catching trout causes the remaining trout to be heavier on average, confirming the estimate.

Explanation: This question demonstrates how convenience sampling based on accessibility can create biased samples in ecological research. The biologists sampled trout from only two easily accessible shoreline locations on a single afternoon, which likely doesn't represent the full population of adult trout in Lake Orion. Fish at different depths, in different parts of the lake, or active at different times may have different weights due to varying food availability, water temperature, or habitat quality. Shoreline fish might be smaller or larger than those in deeper waters. Additionally, sampling on just one afternoon doesn't account for temporal variation. The 1.8 kg mean weight estimate is questionable because the sampling method systematically excludes trout from most of the lake. Valid conclusions would require sampling from multiple locations throughout the lake across different times.

Question 5

1. The conclusion is valid because comparing weekend and weekday study time demonstrates that weekends cause students to study more.
2. The conclusion is not valid because the participants were volunteers from an honors workshop, so the sample may not represent all first-year students. (correct answer)
3. The conclusion is valid because 40 students is enough to generalize to all first-year students.
4. The conclusion is not valid because self-reported study time can never be used in statistics.
5. The conclusion is valid because the study measured the same students twice, eliminating all bias.

Explanation: This question highlights how volunteer samples from specific subgroups cannot support generalizations to larger populations. The researchers recruited volunteers from an honors study-skills workshop, creating a sample that likely overrepresents academically motivated students who actively seek study improvement resources. These students probably have different study habits than typical first-year students, making any conclusions about weekend versus weekday study time invalid for the general first-year population. Additionally, self-selection bias occurs when students choose to participate, further skewing the sample toward those interested in the research topic. To validly answer their research question, researchers would need to randomly sample from all first-year students, not just workshop attendees, and address potential nonresponse issues.

Question 6

1. The conclusion is valid because the surveys were mailed, which prevents any kind of bias.
2. The conclusion is not valid because 620 responses is less than half of 2000, so the sample size is automatically too small.
3. The conclusion is not valid because drivers who received tickets might be less likely to respond, so nonresponse bias could make 18% an underestimate. (correct answer)
4. The conclusion is valid because the agency used random selection, so nonresponse can be ignored.
5. The conclusion is valid because receiving a ticket causes drivers to avoid surveys, proving the estimate is accurate.

Explanation: This question demonstrates how nonresponse bias can specifically undermine conclusions when the characteristic being measured might influence response rates. The transportation agency randomly selected drivers, which is appropriate, but only 31% (620/2000) responded to the mailed survey. Critically, drivers who received speeding tickets might be less likely to respond due to embarrassment, legal concerns, or negative associations with government agencies. This differential nonresponse would cause the 18% estimate to underestimate the true proportion of drivers with speeding tickets. The low response rate combined with the sensitive nature of the question makes the conclusion questionable. A more valid approach might use official records rather than self-reported data, or employ methods to increase response rates and assess nonresponse bias.

Question 7

1. The conclusion is valid because the sample size is large, so the estimate must be close to the true proportion.
2. The conclusion is not valid because the sample is a voluntary response sample and may overrepresent people with strong opinions. (correct answer)
3. The conclusion is valid because posting on the city's accounts gives every adult an equal chance to respond.
4. The conclusion is not valid because 71% support in the sample proves bike lanes will reduce traffic congestion.
5. The conclusion is not valid because the sample size should be at least 10% of the city's adults.

Explanation: This question tests understanding of voluntary response bias in data collection. The city posted a poll on social media, which creates a voluntary response sample where people self-select to participate. This sampling method typically overrepresents people with strong opinions about the topic (bike lanes) and underrepresents those who are neutral or less engaged. The correct answer B identifies this fundamental flaw - voluntary response samples are not representative of the population. When data collection allows self-selection rather than using random sampling, the resulting estimates cannot be trusted to reflect the true population parameter, regardless of how large the sample size is.

Question 8

1. The conclusion is valid because surveying every household in the selected regions eliminates sampling error.
2. The conclusion is not valid because selecting only 2 regions is cluster sampling, and if the chosen regions differ from others, the result may not represent the entire county. (correct answer)
3. The conclusion is valid because cluster sampling always produces a representative sample as long as clusters are geographic.
4. The conclusion is not valid because having high-speed internet causes households to live in the selected regions.
5. The conclusion is not valid because 58% is not a majority, so it cannot be generalized to the population.

Explanation: The skill tested in this AP Statistics question is recognizing limitations in cluster sampling with few clusters, and how it impacts the validity of population inferences. The county selected only 2 out of 10 regions as clusters and surveyed all households within them, but with so few clusters, the sample may not capture county-wide variability if the chosen regions differ from others. Choice C distracts by claiming cluster sampling is always representative for geographic areas, but representativeness depends on random selection and sufficient clusters. Trustworthy conclusions in cluster sampling require enough randomly selected clusters to approximate the population's diversity. This conclusion is invalid due to the small number of clusters, highlighting that inadequate cluster counts can lead to bias similar to non-random sampling.

Question 9

1. The conclusion is not valid because the sample size is only 200; it must be at least 500 to generalize.
2. The conclusion is valid because selecting the same number from each department guarantees no bias, regardless of department sizes.
3. The conclusion may not be valid because sampling equal counts from unequal-sized departments overrepresents smaller departments unless results are weighted or a proportional stratified sample is used. (correct answer)
4. The conclusion is valid because stratifying always makes a sample representative even if strata sizes are ignored.
5. The conclusion is not valid because the survey proves that working from home increases employee productivity.

Explanation: This AP Statistics question focuses on evaluating stratified sampling and the impact of unequal strata sizes on data representativeness, relating to how collection methods influence truthful inferences. The problem arises because the analyst sampled equal numbers from departments of varying sizes, overrepresenting smaller departments and potentially skewing the overall proportion unless weighted adjustments are made. A distractor like choice B misleadingly suggests that equal sampling from strata ensures no bias, but this ignores the need for proportional allocation or weighting in stratified samples. Trustworthy conclusions require that stratified samples reflect the population's composition, either by sampling proportionally or weighting results accordingly to avoid misrepresentation. In this scenario, the conclusion may not be valid without such adjustments, underscoring the mini-lesson that sampling design must align with population structure for accurate generalizations.

Question 10

1. The conclusion is valid because patients at the clinic are a random subset of all adults in the county.
2. The conclusion is not valid because the sample consists of clinic visitors and may not represent all adults in the county (selection bias). (correct answer)
3. The conclusion is valid because 300 is a standard sample size used in many surveys.
4. The conclusion is not valid because getting a flu shot causes people to visit clinics more often.
5. The conclusion is not valid because the nurse should have used a smaller sample to reduce variability.

Explanation: Identifying selection bias in convenience samples is the focus of this AP Statistics question, exploring how data collection methods reveal or distort the truth. The clinic sampled only visitors, who may be more health-conscious and likely to get flu shots, creating a biased group that doesn't represent all county adults. Choice A distracts by claiming clinic patients are random, but they are self-selected and may differ systematically from the population. Trustworthy conclusions require a sampling method that includes non-clinic-goers, such as random digit dialing or address-based sampling. Here, the conclusion is invalid due to selection bias, teaching that samples from specific venues often fail to generalize unless the venue mirrors the population.

Question 11

1. The conclusion is valid because the accounts were randomly selected, so nonresponse cannot create bias.
2. The conclusion is not valid because the sample size of 1200 is too small for a streaming service.
3. The conclusion may not be valid because only 840 of the randomly selected subscribers responded; if responders differ from nonresponders, nonresponse bias could affect the estimate. (correct answer)
4. The conclusion is valid because 72% is based on more than 800 responses, which guarantees representativeness.
5. The conclusion is not valid because recommending the service causes subscribers to check email more often.

Explanation: This AP Statistics question evaluates nonresponse bias in random samples, stressing how incomplete responses affect the truthfulness of data conclusions. Although accounts were randomly selected, only 840 of 1200 responded, and if nonresponders differ (e.g., less satisfied subscribers ignore emails), the results could be biased. Choice A is a distractor suggesting randomness eliminates nonresponse bias, but bias can still occur if responders aren't representative. For trustworthy conclusions, high response rates or follow-ups are needed to mitigate nonresponse, ensuring the responding sample reflects the selected one. The conclusion may not be valid without addressing this, providing a lesson that even random starts require complete data to avoid distortion.

Question 12

1. The conclusion is valid because 600 respondents is large enough to eliminate any bias from the sampling method.
2. The conclusion is not valid because using only landline numbers may undercoverage certain groups of voters, so the sample may not represent all registered voters. (correct answer)
3. The conclusion is valid because calling at random guarantees that every registered voter has an equal chance to be selected.
4. The conclusion is not valid because approval of the measure causes people to have landline phones.
5. The conclusion is not valid because a proportion cannot be estimated without measuring the entire population.

Explanation: This AP Statistics question examines undercoverage bias in sampling frames, particularly with outdated methods like landline surveys, and how it affects the truth of conclusions. The issue is that using only landline numbers excludes cell-phone-only households, which may include younger or mobile voters with different opinions, leading to a non-representative sample of registered voters. Choice C distracts by claiming random calling ensures equal chance, but this overlooks undercoverage if the list misses parts of the population. To ensure trustworthy conclusions, the sampling frame must cover the entire population adequately, using methods like mixed-mode surveys to reach all groups. The conclusion here is invalid due to potential undercoverage, teaching that biases from incomplete frames can distort estimates and must be addressed for accurate results.

Question 13

1. The conclusion is not valid because the first 300 respondents form a voluntary response sample that may differ from students who responded later or not at all. (correct answer)
2. The conclusion is valid because 300 is a sufficiently large sample size for any school.
3. The conclusion is valid because emailing all students guarantees a random sample of those who respond.
4. The conclusion is not valid because eating breakfast causes students to respond to surveys more quickly.
5. The conclusion is not valid because the percentage should have been computed using all 1800 students, not just the 300 who responded.

Explanation: In AP Statistics, this question assesses the ability to recognize voluntary response bias and nonresponse issues in data collection, emphasizing how the method affects the truthfulness of conclusions. The key issue is that the principal used the first 300 responses from an email survey, creating a voluntary response sample where quicker responders might differ from others, such as being more likely to eat breakfast or have strong opinions. Choice B is a distractor that wrongly claims a sample of 300 is always sufficient, disregarding the bias from self-selection and timing. For trustworthy conclusions, surveys should aim for high response rates and random selection to avoid nonresponse bias, where nonresponders might have different characteristics than responders. Here, the conclusion is invalid due to potential differences between early responders and the rest of the student body, teaching that response mechanisms must be considered for accurate population estimates.

Question 14

1. The conclusion is valid because selecting every 20th customer guarantees a simple random sample of all customers.
2. The conclusion is not valid because the sampling frame includes only customers shopping from 5 p.m. to 8 p.m., which may not represent all customers. (correct answer)
3. The conclusion is valid because 900 observations is enough to represent every time period of the day.
4. The conclusion is not valid because using digital coupons causes customers to shop in the evening.
5. The conclusion is not valid because systematic sampling is always biased, regardless of how it is done.

Explanation: This question in AP Statistics tests understanding of systematic sampling and time-based biases in the sampling frame, relating to data collection's impact on truthful insights. The chain sampled every 20th customer only during evening hours, potentially missing daytime shoppers with different coupon habits, thus not representing all customers. Choice A is a distractor that falsely equates systematic sampling with simple random sampling, but systematic methods can be biased if patterns align with the interval. For trustworthy conclusions, systematic sampling should cover the full population variability, including different times if behaviors vary. The conclusion is invalid due to the limited time frame, emphasizing that sampling must encompass all relevant population segments to avoid bias.

Question 15

1. The conclusion is valid because the sample size of 250 is large enough to represent the city.
2. The conclusion is not valid because the sample was a convenience sample from a bike festival and likely overrepresents people who favor bike lanes. (correct answer)
3. The conclusion is valid because asking people who walked by is essentially the same as a simple random sample.
4. The conclusion is not valid because 78% support proves that bike lanes will reduce traffic congestion.
5. The conclusion is not valid because any survey must include at least 1000 people to be accurate.

Explanation: This question tests the skill of identifying sampling bias in data collection methods, specifically convenience sampling, as part of understanding how collected data can tell the truth in AP Statistics. The data collection issue here is that the survey was conducted at a bike festival using a convenience sample of passersby, which likely includes a higher proportion of bike enthusiasts who support bike lanes, leading to an overestimation of citywide support. A common distractor is choice A, which incorrectly assumes that a large sample size alone ensures representativeness, ignoring the bias introduced by the non-random selection method. To draw trustworthy conclusions from survey data, it's essential to use random sampling techniques that give every member of the population an equal chance of being selected, thereby minimizing bias and allowing generalization to the entire population. In this case, the conclusion is invalid because the sample does not represent all adult residents, highlighting the importance of evaluating the sampling frame and method before accepting results.

Question 16

1. The conclusion is valid because 1,860 is a very large sample size, so it must represent all customers.
2. The conclusion is not valid because the QR code creates a voluntary response sample, and people with strong opinions may be more likely to respond. (correct answer)
3. The conclusion is valid because using a 1-to-5 scale guarantees an unbiased estimate of the mean.
4. The conclusion is not valid because satisfaction ratings should be measured on a 1-to-10 scale instead.
5. The conclusion is valid because high satisfaction causes people to scan QR codes, confirming the average is high.

Explanation: This question examines voluntary response bias in customer satisfaction surveys, a common issue in business research. By printing QR codes on receipts and relying on customers to voluntarily scan and respond, the restaurant creates a sample biased toward customers with strong opinions (either very satisfied or very dissatisfied). Moderately satisfied customers are less motivated to take time to complete surveys, leading to overrepresentation of extreme views. The large sample size (1,860) doesn't correct this fundamental bias in who chooses to respond. The 4.6 average likely overestimates true satisfaction if happy customers are more motivated to share positive experiences. For valid conclusions, the restaurant would need to randomly select customers and actively solicit their feedback, perhaps offering incentives to increase response rates across all satisfaction levels.

Question 17

1. The conclusion is valid because a systematic sample from a complete employee list can be representative if there is no pattern related to satisfaction in the ordering. (correct answer)
2. The conclusion is not valid because systematic sampling is always biased compared with random sampling.
3. The conclusion is not valid because 196 responses is not enough to estimate a proportion accurately.
4. The conclusion is valid because satisfaction with insurance causes employees to respond to surveys, ensuring a correct estimate.
5. The conclusion is not valid because the sample should have included exactly half of all employees.

Explanation: This question tests understanding of systematic sampling and its potential validity. The HR department used systematic sampling (every 10th person from an alphabetized list), which can produce representative samples if the list ordering is unrelated to the characteristic being measured. Since alphabetical order of names is unlikely to correlate with health insurance satisfaction, this method should yield results similar to simple random sampling. The high response rate (196/210 = 93%) minimizes nonresponse bias concerns. The conclusion that 72% of employees are satisfied appears valid, assuming the employee list was complete and current. Systematic sampling is often more practical than simple random sampling while maintaining statistical validity, making it appropriate for this internal company survey.

Question 18

1. The conclusion is valid because the original selection was random from the full subscriber list, making the sample likely representative, though nonresponse could still introduce bias. (correct answer)
2. The conclusion is not valid because 742 responses is too small to estimate a percentage for a large subscriber base.
3. The conclusion is not valid because only people who like subtitles would respond to the email, so it must be biased.
4. The conclusion is valid because emailing a survey guarantees that every subscriber has an equal chance to respond.
5. The conclusion is valid because turning subtitles on causes people to watch more, so preference must be common.

Explanation: This question illustrates how nonresponse bias can affect conclusions even when the initial sample selection is random. The streaming service correctly started with a random sample of 1200 subscribers from their database, which is good practice. However, only 742 responded (about 62% response rate), introducing potential nonresponse bias if those who responded differ systematically from non-responders in their subtitle preferences. Despite this concern, the conclusion has some validity because the original selection was random and the response rate is reasonably high. The 55% estimate may be somewhat biased but is likely more accurate than samples from voluntary response or convenience sampling. To improve validity, the company could investigate whether responders and non-responders differ in relevant characteristics.

Question 19

1. The conclusion is valid because 312 responses is a large sample, so the sample proportion should be close to the population proportion.
2. The conclusion is not valid because the data come from a voluntary response sample from Instagram followers, which may not represent all Central High students. (correct answer)
3. The conclusion is valid because the poll asked a clear question and used the same wording for everyone.
4. The conclusion is not valid because a proportion cannot be estimated unless at least 1000 students respond.
5. The conclusion is valid because the poll shows that later start times cause students to be more supportive of school.

Explanation: This question tests understanding of how voluntary response samples affect the validity of statistical conclusions. The school newspaper posted a poll on Instagram, which creates a voluntary response sample where only followers who see the story and choose to respond are included. This sampling method likely overrepresents students who follow the newspaper (possibly more engaged students) and those with strong opinions about start times. While 312 responses seems substantial, sample size alone doesn't fix bias from non-representative sampling. To make valid conclusions about all Central High students, the newspaper would need a sampling method that gives every student an equal chance of being selected, such as a simple random sample from the student directory.

Question 20

1. The conclusion is not valid because a convenience sample of clinic patients may not represent all adults in the county. (correct answer)
2. The conclusion is valid because 150 observations are enough to guarantee representativeness.
3. The conclusion is not valid because measuring blood pressure causes it to increase, so the mean is inflated.
4. The conclusion is valid because patients are randomly distributed throughout the county.
5. The conclusion is not valid only because January is too short a time period to compute an average.

Explanation: This question illustrates classic convenience sampling bias in health research. The clinic sampled only patients who visited in January, creating a biased sample that likely overrepresents people with health concerns serious enough to seek medical care. Choice A correctly identifies that clinic patients are not representative of all county adults - they probably include more people with health issues, potentially including hypertension, compared to the general population. The sample size of 150 is reasonable for estimating a mean, and measuring blood pressure doesn't significantly affect the reading in a way that would invalidate results. Random distribution of patients geographically doesn't make them representative of all adults. To validly estimate county-wide blood pressure levels, researchers need a random sample from the entire adult population, not just those seeking medical care.