AP Statistics Unit 3: Collecting Data Practice Exam

Assessment for Unit 3: Collecting Data

Estimated Time: 60 minutes

Exam Details

Questions: 19 total (19 multiple choice)
Time: 60 minutes (recommended)
Topics Covered: Unit 3: Collecting Data
Format: Multiple Choice questions matching real exam difficulty
Scoring: Instant results with detailed explanations

A. Multiple-Choice Questions (19 Questions)

Select the one best answer for each question.

1. A university administrator wants to determine the average amount of money students at the university spend on textbooks per semester. The administrator obtains a list of all 15,000 currently enrolled students. From this list, 200 students are selected at random and surveyed about their textbook spending. Which of the following best describes the population of interest in this setting?

(A)The 200 students who were selected and surveyed.(B)The 15,000 currently enrolled students at the university.(C)The average amount of money spent on textbooks by the 200 students.(D)All university students in the country.

2. A local television news station asks its viewers to visit their website and vote 'Yes' or 'No' on the question: 'Do you support the construction of a new sports stadium in the downtown area?' Over the course of the evening news broadcast, 3,500 votes are cast, with 78% voting 'No'. Which of the following best explains why the results of this poll are likely unreliable?

(A)The sample size of 3,500 is too small to be statistically significant for a city-wide issue.(B)The survey did not include a 'Not Sure' or 'Undecided' option, forcing a binary choice.(C)The sample is a voluntary response sample, likely overrepresenting individuals with strong negative opinions about the stadium.(D)The poll was conducted online, excluding residents who do not have access to the internet, which is the only source of bias.

3. To investigate the study habits of students at a large high school, a mathematics teacher distributes a survey to all students in her AP Calculus classes. She analyzes the data from the 55 students who return the survey and uses the results to estimate the average study time for all students in the high school. Which of the following describes the most significant flaw in this data collection method?

(A)The sample size is too small relative to the population of the high school.(B)The teacher used a census instead of a sample, making the data difficult to analyze.(C)The sample is a convenience sample, and AP Calculus students likely have different study habits than the general student population.(D)The teacher should have used an experiment rather than an observational study to determine study habits.

4. A study examined the relationship between daily coffee consumption and heart health. Researchers surveyed 2,000 randomly selected adults from a large city and asked about their daily coffee intake. The researchers then accessed the medical records of these adults to check for heart disease markers. The study found that adults who drank 2 or more cups of coffee daily had significantly lower markers for heart disease than those who drank less or no coffee. Which of the following is the most appropriate conclusion?

(A)Drinking coffee causes a reduction in heart disease markers for all adults in the city.(B)Drinking coffee causes a reduction in heart disease markers, but only for the adults in the sample.(C)There is an association between drinking coffee and lower heart disease markers in the population of adults in the city, but a causal relationship cannot be established.(D)The study is an experiment, so a causal relationship can be established between coffee consumption and heart health.

5. A high school principal wants to determine if students would prefer a longer lunch break or an earlier dismissal time. The principal obtains a list of all 1,200 students in the school and uses a random number generator to select 100 distinct student ID numbers. The students corresponding to these IDs are surveyed. Which of the following best describes the scope of inference for this study?

(A)The results can be generalized to all students at this high school, and a cause-and-effect relationship can be determined.(B)The results can be generalized to all students at this high school, but a cause-and-effect relationship cannot be determined.(C)The results cannot be generalized to the population because the sample size is too small relative to the population.(D)The results apply only to the 100 students in the sample because it was an observational study.

6. A materials engineer is testing two different formulations of concrete, Type A and Type B, to see which is stronger. She has 40 identical concrete molds. She uses a coin flip for each mold to determine whether it will be filled with Type A or Type B concrete, resulting in 20 molds of each type. After the concrete cures, she measures the crushing strength of each block. Which of the following statements is true?

(A)This is an observational study because the engineer simply observed the strength of the concrete.(B)This is an observational study because the concrete molds were not randomly selected from all possible molds.(C)This is an experiment because the engineer randomly assigned the treatments (concrete types) to the experimental units (molds).(D)This is an experiment because the sample size was large enough to ensure statistical significance.

7. [Skill: 1.C | Topic: 3.3] An airline wants to conduct a customer satisfaction survey regarding the comfort of its seats. The airline operates 50 flights per day from a specific airport. To select the sample, the operations manager randomly selects 5 of these flights and surveys every passenger on the selected flights. Which of the following best describes this sampling method?

(A)Simple random sampling(B)Stratified random sampling(C)Cluster sampling(D)Systematic random sampling

8. [Skill: 1.C | Topic: 3.3] A high school principal wants to select a simple random sample (SRS) of 20 students from the senior class of 400 students to serve on a graduation committee. Which of the following procedures results in a simple random sample?

(A)Select the first 20 seniors who arrive at school on Monday morning.(B)List all seniors alphabetically, select a random starting point among the first 20 names, and then select every 20th student on the list.(C)Divide the seniors into two groups by gender (male and female). Randomly select 10 students from the male group and 10 students from the female group.(D)Assign each senior a unique integer from 1 to 400. Use a random number generator to select 20 unique integers and choose the students corresponding to those numbers.

9. [Skill: 4.A | Topic: 3.3] A zoologist is studying the weight of a specific species of turtle in a large wetland area. The area consists of two distinct habitats: a riverbank zone where food is abundant and a deep-water zone where food is scarce. The zoologist suspects that turtles living in the riverbank zone are significantly heavier than those in the deep-water zone. To estimate the mean weight of the turtle population, the zoologist decides to use a stratified random sample, using the habitats as strata, rather than a simple random sample. What is the primary advantage of using this method in this context?

(A)It eliminates the need for randomization within the selection process.(B)It reduces the variability of the estimate by ensuring proportional representation from groups that are homogeneous with respect to weight.(C)It is less expensive and time-consuming to implement than a simple random sample.(D)It allows the zoologist to establish a cause-and-effect relationship between habitat and weight.

10. A local school board wants to assess parent opinion regarding a proposal to extend the school day by 30 minutes. The board obtains a list of all households with children enrolled in the district. They select a simple random sample of 500 households and mail a survey to each selected household. Of the 500 surveys mailed, 85 are returned. The results indicate that 78% of the respondents oppose the extension of the school day. Which of the following describes the most significant potential source of bias in this survey?

(A)Undercoverage bias, because households without children in the district were not included in the sampling frame.(B)Voluntary response bias, because the parents chose whether or not to return the survey.(C)Nonresponse bias, because a large proportion of the selected sample did not return the survey.(D)Response bias, because the wording of the question likely influenced the parents' answers.

11. A television news program invites viewers to visit their website to vote on whether they support a new tax law. The website records 12,400 votes, with 88% voting 'No.' The news anchor claims that 'an overwhelming majority of the public opposes the new tax law.' Which of the following is the most valid criticism of this conclusion?

(A)The sample size is too small to draw a statistically significant conclusion.(B)The survey results are flawed due to voluntary response bias, as those with strong negative opinions are more likely to participate.(C)The survey suffers from nonresponse bias because not everyone who visited the website voted.(D)The large sample size ensures precision, but sampling variability suggests the true proportion is slightly less than 88%.

12. A researcher is conducting a study on dental hygiene habits. She interviews a random sample of 200 adults face-to-face. One of the questions asked is: 'Do you brush your teeth at least twice a day, as recommended by dentists?' The results show that 95% of the subjects answered 'Yes.' A subsequent audit of dental records suggests the true proportion is much lower. What type of bias most likely accounts for this discrepancy?

(A)Undercoverage bias(B)Nonresponse bias(C)Response bias(D)Sampling variability

13. [Skill: 1.B | Topic: 3.5] A botanist is studying the effects of soil acidity and irrigation frequency on the yield of a specific tomato variety. The botanist intends to test three distinct levels of soil acidity (pH 5.5, 6.5, and 7.5) and two distinct levels of irrigation frequency (daily and weekly). A total of 60 tomato plants are available for the study. If the botanist wants to test every combination of these conditions using a completely randomized design, which of the following correctly identifies the experimental units, the factors, and the number of treatments?

(A)Experimental units: 60 plants; Factors: Soil acidity and irrigation frequency; Treatments: 5(B)Experimental units: 60 plants; Factors: Soil acidity and irrigation frequency; Treatments: 6(C)Experimental units: The tomato yield; Factors: pH 5.5, 6.5, 7.5, daily irrigation, weekly irrigation; Treatments: 2(D)Experimental units: The tomato yield; Factors: Soil acidity and irrigation frequency; Treatments: 6

14. [Skill: 1.C | Topic: 3.5] A veterinary researcher wants to evaluate the effectiveness of a new flea collar compared to a standard collar. The study involves 100 dogs of various breeds and sizes. The researcher suspects that the effectiveness of the collars may depend heavily on the size of the dog (Small, Medium, or Large). Which of the following experimental designs is most appropriate to account for the variability in collar effectiveness due to dog size?

(A)A completely randomized design where each of the 100 dogs is assigned to either the new collar or the standard collar using a random number generator.(B)A matched pairs design where each dog wears the new collar for one month and the standard collar for the next month, with the order randomized.(C)A randomized block design where dogs are separated into three groups based on size (Small, Medium, Large), and within each size group, dogs are randomly assigned to either the new or standard collar.(D)A stratified random sample where dogs are selected from each size group and then all selected dogs are given the new collar to observe its effectiveness.

15. [Skill: 1.C | Topic: 3.5] A running shoe company wants to test the durability of a new rubber compound for soles compared to the current compound. They recruit 40 competitive runners for the study. Which of the following descriptions outlines a **matched pairs design**?

(A)The runners are listed alphabetically. The first 20 receive shoes with the new compound, and the next 20 receive shoes with the current compound.(B)Each runner receives a pair of shoes where one shoe has the new compound sole and the other has the current compound sole. The side (left or right) for the new compound is determined randomly for each runner.(C)The runners are blocked by their weekly mileage (High vs. Low). Within each block, half are randomly assigned to wear the new compound shoes and half to wear the current compound shoes.(D)The names of all 40 runners are placed in a hat. The first 20 names drawn are assigned to the new compound group, and the remaining 20 are assigned to the current compound group.

16. A biologist is conducting an experiment to compare the effects of two different fertilizers, A and B, on the growth of tomato plants. The biologist has 40 tomato plants available for the study. Half of the plants are of the 'Big Boy' variety, which naturally grows tall, and the other half are of the 'Roma' variety, which is naturally shorter. The biologist suspects that the variety of the tomato plant will strongly influence the growth height regardless of the fertilizer used. Which of the following experimental designs is most appropriate to isolate the effect of the fertilizers?

(A)A completely randomized design where the 40 plants are assigned to the two fertilizer groups using a random number generator.(B)A matched pairs design where each 'Big Boy' plant is paired with a 'Roma' plant, and one receives Fertilizer A while the other receives Fertilizer B.(C)A randomized block design where the plants are separated by variety, and within each variety, half are randomly assigned to Fertilizer A and half to Fertilizer B.(D)A stratified random sample where 10 'Big Boy' and 10 'Roma' plants are selected, and all 20 are given Fertilizer A to establish a baseline.

17. A medical researcher is testing a new medication for lowering blood pressure against a current standard drug. The subjects available for the study include both men and women of varying ages. The researcher believes that age has a significant impact on how the body metabolizes these drugs, but gender does not. Why would a randomized block design blocking by age group be preferred over a completely randomized design?

(A)Blocking by age eliminates the effects of all lurking variables, ensuring that the only difference between groups is the medication.(B)Blocking by age ensures that the sample is perfectly representative of the population's age distribution.(C)Blocking by age reduces the variability in the response variable within each block, making it easier to detect a difference between the two medications if one exists.(D)Blocking by age prevents the placebo effect from influencing the results of the experiment.

18. A cognitive psychologist recruits 60 volunteers from a local university to participate in a study about the effects of caffeine on memory. The psychologist randomly assigns 30 of the volunteers to consume a caffeinated beverage and the other 30 to consume a placebo beverage. After one hour, all participants complete a memory test. The results show that the group who consumed caffeine had a statistically significantly higher average score on the memory test than the group who consumed the placebo. Based on the design of the study, which of the following conclusions is appropriate?

(A)Caffeine consumption causes improved memory performance for all students at the local university.(B)Caffeine consumption causes improved memory performance for the 60 volunteers in the study.(C)There is an association between caffeine consumption and improved memory performance for all students at the local university, but causation cannot be established.(D)There is an association between caffeine consumption and improved memory performance for the 60 volunteers in the study, but causation cannot be established.

19. A city council wants to determine if there is a relationship between the proximity of a resident's home to a public park and the resident's self-reported happiness level. The council selects a simple random sample of 1,000 residents from the city's population registry. They measure the distance from each resident's home to the nearest park and administer a survey to measure happiness levels. The data reveals a strong, statistically significant negative correlation between distance to a park and happiness level. Which of the following is the most appropriate conclusion?

(A)Living closer to a park causes residents of this city to have higher happiness levels.(B)Living closer to a park is associated with higher happiness levels for residents of this city, but causation cannot be established.(C)Living closer to a park causes higher happiness levels, but the result applies only to the 1,000 residents in the sample.(D)Living closer to a park is associated with higher happiness levels, but the result applies only to the 1,000 residents in the sample.

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