AnswersSS Integrated Math IIB 2026Probability with Combinations and Permutations

Considerations When Sampling Answers

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1
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Many large cities have considered or passed proposals that ban the use of plastic grocery bags in stores. A concerned student would like to measure if residents of her hometown would consider a similar ban on plastic bags. Standing in a busy shopping area, the student approaches adults and asks, "Items made of plastics are a dangerous, growing source of pollution to our world’s oceans and threaten many animal species. Given this, would you support a ban on plastic shopping bags in our city stores?” How might the results of this survey be biased in estimating the proportion of all town residents who would support a ban on plastic bags?

A
The student may overestimate support for a plastic bag ban because only adults in the shopping area were chosen to participate.
B
The student may overestimate support for a plastic bag ban because the wording of the question may influence adults to support a ban.
C
The student may underestimate support for a plastic bag ban because the wording of the question may influence adults to not support a ban.
D
The student may underestimate support for a plastic bag ban because some adults may not want to answer questions about the environment.
2
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Residents of a community currently pay a fee for recreational services in their neighborhood, such as tennis courts, running trails, and a pool. To assess whether there is support for raising the fee for the upcoming summer, a random sample of 50 residents is contacted and asked this question: "Would you support a $10 increase in the recreational fee to support programs for the health and well-being of children in the community?” Of the 50 residents contacted, 42 approved of the fee increase. Which statement describes a likely source of bias present in the survey results?

A
There may be little bias in the results because a random sample of residents was taken.
B
Question wording bias may be present because the question leads those responding toward a certain response.
C
Nonresponse bias may be present because many who support the fee increase may choose to not respond.
D
Undercoverage bias may be present because some parts of the community may not be represented in the survey results.
3

Many large cities use taxes on entertainment tickets to pay for improvements to public facilities, like stadiums, arenas, and concert venues. A city council proposal would increase the current ticket tax in order to raise funds for a new public concert hall. Council representatives plan to conduct a survey outside of a large concert in the summer and ask selected adults if they would support an increase in the ticket tax to pay for the new concert hall. Which type of bias will most likely affect the survey results?

A
This is response bias because it is likely that many who respond will not provide a truthful opinion of the ticket tax.
B
This is undercoverage bias because only those attending the concert will have an opportunity to register an opinion.
C
This is nonresponse bias because many who are asked about the ticket tax may choose to not provide a response.
D
This is voluntary response bias because many vocal supporters of the ticket tax may demand to register their opinion.
4

A random sample of adults in a large US city responded to a series of questions about their use of public transportation. The results of the survey showed that 520 of the 838 adults in the sample (62%) have used public transportation in the past week. How might the results of the survey be biased in obtaining an estimate of all US residents who use public transportation?

A
Because not all residents in this US city were asked to participate, the survey may underestimate usage of public transportation.
B
Because the sample includes only residents in one US city, the survey may overestimate the proportion of US adults who use public transportation.
C
Because those surveyed may choose not to answer, the survey may underestimate the proportion of US residents who use public transportation.
D
Because the survey includes a random sample of residents in one US city, the survey should provide an accurate estimate of the proportion of US adults who use public transportation.
7

A business developer would like to purchase an abandoned corner lot in a small town and build a small convenience store with gasoline pumps on the site. Town leaders are concerned about potential traffic and noise impact to the adjacent neighborhood and send printed surveys to 500 homes in the affected area. Of the 123 surveys returned, 87% oppose the plan to develop the corner lot. How could the sampling design cause town leaders to overestimate or underestimate overall support of the development plan?

A
The leaders may underestimate support because only 123 surveys were returned.
B
The leaders may overestimate overall support because many residents who did not receive surveys will support the plan.
C
The leaders may underestimate overall support because many residents who support the plan may be less likely to respond.
D
The leaders may underestimate support because it can be assumed that all residents who did not return the surveys would support the plan.
8

A city government is considering raising the local income tax to pay for improvements to government facilities. A private citizen opposes the plan and stands on a busy street to survey residents with the question, "Do you agree that wasteful spending is a serious problem in our local government?” The results of the survey will most likely suffer from which type of bias?

A
This is nonresponse bias because many who are asked the question may choose not to respond.
B
This is question wording bias because the question leads those surveyed toward a desired response.
C
This is voluntary response bias because those with a passionate opinion may choose to participate.
D
This is undercoverage bias because many in the population will not have the opportunity to register an opinion.

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