Sampling and Observational Studies

1. The state Department of Transportation wants to know about out-of-state vehicles that pass over a toll bridge with several lanes. A camera installed over one lane of the bridge photographs the license plate of every tenth vehicle that passes through that lane.

Identify the population and sample in this setting.

Choose 1 answer:

(A) The population is all of the vehicles that pass over the toll bridge; the sample is vehicles from the lane with the camera.

(B) The population is all of the vehicles that pass through the lane with the camera; the sample is the group of every tenth vehicle that passes through the lane.

(C) The population is all of the out-of-state vehicles; the sample is the vehicles that pass over the toll bridge.

2. A group of librarians is interested in the numbers of books and other media that patrons check out from their library. They examine the checkout records of $150$ randomly selected adult patrons.

Identify the population and sample in this setting.

Choose 1 answer:

(A) The population is all adult patrons of the library; the sample is the $10$ patrons selected.

(B) The population is all patrons of the library; the sample is the adult patrons of the library.

(C) The population is all patrons who check out at least $1$ book from the library; the sample is the $150$ patrons selected.

3. A pediatrician randomly selected $10$ parents of his patients. Then he surveyed the parents about their opinions of different kinds of diapers.

Identify the population and sample in this setting.

Choose 1 answer:

(A) The population is the parents of the pediatrician's patients who wear diapers; the sample is the parents of all of the pediatrician's patients.

(B) The population is the pediatrician's patients; the sample is the $10$ patients selected.

(C) The population is the parents of the pediatrician's patients; the sample is the $10$ parents of patients selected.

4. A city council member wanted to know how her constituents felt about a planned rezoning. She randomly selected $75$names from the city phone directory and conducted a phone survey.

Identify the population and sample in this setting.

Choose 1 answer:

(A) The population is everyone listed in the city phone directory; the sample is the $75$ people selected.

(B) The population is residents of the city; the sample is the registered voters in the city.

(C) The population is registered voters in the city; the sample is everyone listed in the city phone directory.

1. The population is all of the vehicles that pass through the lane with the camera; the sample is the group of every tenth vehicle that passes through the lane.

2. The population is all adult patrons of the library; the sample is the $150$ patrons selected.

3. The population is the parents of the pediatrician's patients; the sample is the $10$ parents of patients selected.

4. The population is everyone listed in the city phone directory; the sample is the $75$ people selected.

 1. Kara, who lives in Canada, plays a popular online video game where every round has a winner. Her best streak is $21$ wins in a row, and she wonders how that compares to other players. The game's website has a worldwide leaderboard of players with the longest win streaks for each month. Kara finds that the top $200$ longest streaks in the world in June had an average of about $63$ wins in a row.

For which population is $63$ wins a legitimate estimate of the average longest streak?

Choose 1 answer:

(A) Only the top $200$ longest streaks worldwide in June

(B) Only the top $200$ longest streaks in Canada in June

(C) Only the top $200$ longest streaks worldwide from all time

(D) Only the top $200$ longest streaks in Canada from all time

(E) The longest streaks for all players worldwide in June

2. An administrator at a large university is curious how students rate the quality of the athletic facilities at the university. They decide to survey a random sample of $80$ students who participate in the university's intramural football league. The survey shows that $54 \%$ of those asked said they were "very satisfied" with the athletic facilities.

For which population is $54 \%$ a legitimate estimate of the percent of students that are "very satisfied" with the athletic facilities?

Choose 1 answer:

(A) Only students in the survey

(B) All students at the university who participate in the intramural football league

(C) All students at the university, but only those who play an intramural sport

(D) All students at the university, but only those who use the athletic facilities

(E) All students at the university

3. A large gym with hundreds of members offers yoga classes. Members are free to take these classes at no charge, but not all members are interested, and some never take advantage of the yoga classes. Nonmembers can also take these classes, but they must pay a fee for each class.

A manager at the gym is curious about overall satisfaction with these yoga classes, so they survey a large random sample of anyone who has taken a yoga class at the gym in the past year. They find that $78 \%$ of those surveyed are "very satisfied" with the yoga classes.

For which population is $78 \%$ a legitimate estimate of the percent of people that are "very satisfied" with the yoga classes?

Choose 1 answer:

(A) Only those surveyed

(B) All members who have taken a yoga class at the gym in the past year, but not non-members

(C) All non-members who have taken a yoga class at the gym in the past year, but not members

(D) Anyone who has taken a yoga class at the gym in the past year, but not before that

(E) Anyone who has ever taken a yoga class at the gym

4. A news program invites its viewers to call in and share their position on a proposed tax increase. Ninety percent of the viewers that call in say that they will vote against the tax increase.

For which population is $90 \%$ a legitimate estimate of the percent of voters who will vote against the tax increase?

Choose 1 answer:

(A) Only those viewers who called in

(B) Only viewers of this particular episode

(C) Only regular viewers of the show

(D) Only those who have watched this show at some point

(E) All voters

5. First-year students at a certain large university are required to live on campus in $1$ of the $24$ available residence halls. After their first year, students have the option to live away from campus, but many choose to continue living in the residence halls. Estella oversees $12$ of these residence halls. Her department surveyed a large simple random sample of first-year students who live in those $12$ residence halls about their overall satisfaction with campus living.

Estella can safely generalize the results of the survey to which population?

Choose 1 answer:

(A) Only those students who were surveyed

(B) All first-year students, but only those who live in these $12$ residence halls

(C) All students (first-year and not), but only those who live in these $12$ residence halls

(D) All first-year students at the entire university, but not students beyond their first-year

(E) All students at the university

6. Ava is considering moving to a neighborhood in a different city and state than where she currently lives. To better understand home prices in that area, she looks up the values for a large random sample of homes in that city and calculates their average price.

Ava can safely generalize this result to which population?

Choose 1 answer:

(A) Only homes in the sample

(B) All homes in that neighborhood, but not the entire city

(C) All homes in that city, but not the entire state

(D) All homes in the entire state, but not the entire country

(E) All homes in the entire country

7. Various types of doctors attended a large medical conference. Someone leading a session asked the $30$ doctors in attendance how many years of experience they each had. The $15$ dermatologists at the session had an average of $8$ years of experience.

For which population is 8 years a legitimate estimate of the average experience?

Choose 1 answer:

(A) The dermatologists at that session only

(B) All doctors at that session only

(C) All dermatologists at that conference only

(D) All doctors at that conference only

(E) All dermatologists

1. Only the top $$$200$ longest streaks worldwide in June

The $200$ longest streaks weren't randomly selected from a larger population. They are not representative of all players in the world or Canada-they are the top $200$ longest streaks of all players.

2. All students at the university who participate in the intramural football league

Since the sample was randomly selected from students who participate in the university's intramural football league, the results can safely be generalized to this population.

3. Anyone who has taken a yoga class at the gym in the past year, but not before that

Since the sample was randomly selected from anyone who had taken a yoga class at the gym in the past year, the results can safely be generalized to this population.

4. Only those viewers who called in

The viewers who called in weren't randomly selected, and they are likely not representative of any larger group. Viewers who took the time to call in likely have stronger opinions than those who didn't call in, or different opinions than those who don't watch this show.

5. All first-year students, but only those who live in these $12$ residence halls

Since the sample was randomly selected from first-year students who live in those residence halls, the results can safely be generalized to this population.

6. All homes in that city, but not the entire state

Since the sample was randomly selected from all homes in that city, the results can safely be generalized to this population.

7. The dermatologists at that session only

The $15$ dermatologists at this session weren't randomly selected from a larger population. They may not be representative of all doctors or even all dermatologists on the question of experience.

1. Angela created and maintains an exercise app where users log their workouts. She wonders if sending users a daily notification that reminds them to use the app will result in them logging more workouts. She releases an update to her app so that half of users will have daily notifications and the other half won't have daily notifications (randomly determined for each user). After a few weeks, she'll see if one group logs more workouts on average than the other group.

What type of study is this, and what is the response variable?

Choose 1 answer:

(A) An observational study where the number of workouts is the response variable

(B) An observational study where notification presence is the response variable

(C) An experiment where the number of workouts is the response variable

(D) An experiment where notification presence is the response variable

2. According to a study published in the journal Social Psychological and Personality Science, people with religious affiliations live longer, on average, than those without religious affiliations. The study analyzed more than $1,000$ obituaries and accounted for other variables like sex and marital status.

What type of study is this, and what is the explanatory variable?

Choose 1 answer:

(A) An observational study where lifespan is the explanatory variable

(B) An observational study where religious affiliation is the explanatory variable

(C) An experiment where lifespan is the explanatory variable

(D) An experiment where religious affiliation is the explanatory variable

3. A group of researchers wants to know whether graduates from different teacher preparation programs are more likely to stay in the profession. They select a stratified random sample of this year's graduates from several programs. The researchers will contact the graduates after $1, 5,$ and $10$ years to see whether they are teaching in those years.

What type of observational study is this?

Choose 1 answer:

(A) A retrospective study

(B) A prospective study

(C) A sample survey

(D) None of these. It's an experiment, not an observational study.

4. The library where Kara works is planning to add a maker space where members can share equipment and services to create crafts. Kara randomly selected members from their database, then contacted them to ask what kinds of equipment and services they would be most likely to use.

What type of observational study is this?

Choose 1 answer:

(A) A retrospective study

(B) A prospective study

(C) A sample survey

(D) None of these. It's an experiment, not an observational study.