20 easy SAT Inference from samples & margin of error questions

In a nationwide poll of 900 randomly selected adults, 42% indicated they use public transportation regularly, with a margin of error of 3.3 percentage points. A researcher claims that fewer than 40% of all adults use public transportation regularly. Is this claim supported by the poll results?

• ANo, because the confidence interval ranges from 38.7% to 45.3%, which includes values above 40%.
• BYes, because 42% is greater than 40%, proving the claim is false.
• CYes, because the margin of error of 3.3 percentage points is less than the difference between 42% and 40%.
• DNo, but if the sample size were smaller, the claim would be supported.

A health organization randomly selected 320 registered voters from all registered voters in Lincoln County and surveyed them about their exercise habits. What is the largest population to which the results of this survey can be generalized?

• AAll adults in Lincoln County
• BAll registered voters in the state
• CThe 320 registered voters who were surveyed
• DAll registered voters in Lincoln County

A poll of 900 randomly selected adults found that 38% prefer brand A over brand B, with a margin of error $of \pm 3$ percentage points. If the sample size were increased to 3600 adults, which of the following best describes what would happen to the margin of error?

• AIt would remain $approximately \pm 3$ percentage points.
• BIt would decrease to $approximately \pm 1.5$ percentage points.
• CIt would increase to $approximately \pm 6$ percentage points.
• DIt would decrease to $approximately \pm 0.75$ percentage points.

A survey of 400 randomly selected voters found that 51% support Candidate A, with a margin of error of 5 percentage points. A second survey of 400 randomly selected voters found that 48% support Candidate B, with a margin of error of 5 percentage points. Which of the following conclusions is most appropriate?

• ACandidate A has more support than Candidate B.
• BCandidate B has more support than Candidate A.
• CThe levels of support for the two candidates cannot be distinguished based on these surveys.
• DIf each survey used 800 voters, Candidate A would have more support than Candidate B.

A political poll of 800 randomly selected likely voters found that 49% plan to vote for Candidate X, with a margin of error $of \pm 3.5$ percentage points. Which of the following best describes what the margin of error represents?

• AThe difference between the highest and lowest possible percentages in the confidence interval is 3.5 percentage points.
• BThe percentage of likely voters who plan to vote for Candidate X could be as low as 49% or as high as 52.5%.
• CThe true percentage of all likely voters who plan to vote for Candidate X is likely between 45.5% and 52.5%.
• DIf the sample size were doubled, the margin of error would decrease to $approximately \pm 1.75$ percentage points.

A librarian randomly selected 225 members from all members of the downtown public library and surveyed them about their reading preferences. What is the largest population to which the results of this survey can be generalized?

• AThe 225 library members who were surveyed
• BAll residents of the downtown area
• CAll members of the downtown public library
• DAll public library members in the city

A polling organization surveyed 900 randomly selected adults and found that 48% favor a new policy, with a margin of error of 3 percentage points. A second survey of 225 randomly selected adults on the same policy would most likely have a margin of error closest to which of the following?

• A1.5 percentage points
• B3 percentage points
• C4.5 percentage points
• D6 percentage points

A poll found that 72% of 1200 randomly selected adults support a new policy, with a margin of error of 3 percentage points. Another poll found that 68% of 1200 randomly selected adults from the same population support a different policy, with a margin of error of 3 percentage points. Based on these results, which of the following is true?

• AMore adults support the new policy than the different policy.
• BThe two policies have equal support among adults.
• CThe confidence intervals for the two percentages overlap, so the difference in support cannot be determined.
• DIf each poll used 2400 adults instead, the difference between the two percentages would be smaller.

A survey of 400 randomly selected voters found that 62% support a proposed ballot measure, with a margin of error of 5 percentage points. Based on this information, which of the following is most likely true about the percentage of all voters who support the measure?

• AIt is exactly 62%.
• BIt is between 57% and 67%.
• CIt is between 57% and 62%.
• DIt would be between 52% and 72% if 800 voters were surveyed instead.

A researcher randomly selected 150 students from all students enrolled at Central High School and surveyed them about their study habits. What is the largest population to which the results of this survey can be generalized?

• AAll students enrolled at Central High School
• BAll high school students in the district
• CThe 150 students who were surveyed
• DAll students in the United States

In a survey of 2500 randomly selected residents, 33% indicated they support a proposed tax increase, with a margin of error $of \pm 2$ percentage points. If researchers want to reduce the margin of error $to \pm 1$ percentage point, approximately how many residents should be surveyed?

• A$5000$
• B$10000$
• C$1250$
• D$7500$

A survey of 2500 randomly selected households found that 38% own a pet, with a margin of error of 2 percentage points. Another survey of 2500 randomly selected households found that 42% recycle regularly, with a margin of error of 2 percentage points. Based on these results, which of the following statements is justified?

• AMore households recycle regularly than own a pet.
• BThe same percentage of households own a pet and recycle regularly.
• CIt cannot be determined whether more households recycle regularly than own a pet.
• DIf the sample size for each survey were doubled, the difference between the two percentages would increase.

A medical study surveyed 800 randomly selected patients and found that 55% experienced symptom improvement, with a margin of error of 3.5 percentage points. Based on this survey, what is the lowest percentage of all patients who might experience symptom improvement?

• A51.5%
• B55%
• C3.5%
• DIf the sample size were increased to 1600 patients, the lowest percentage would increase.

A school district randomly selected 340 parents from all parents of students enrolled in elementary schools in the district and surveyed them about after-school programs. What is the largest population to which the results of this survey can be generalized?

• AAll parents in the district
• BAll parents of students enrolled in elementary schools in the district
• CAll parents of students enrolled in schools in the district
• DThe 340 parents who were surveyed

A survey of 400 randomly selected employees at a company found that 65% are satisfied with their work-life balance, with a margin of error $of \pm 5$ percentage points. Another survey of 400 randomly selected employees at a different company found that 58% are satisfied with their work-life balance, with a margin of error $of \pm 5$ percentage points. Based on these surveys, which of the following conclusions is most appropriate?

• AThe first company has a higher satisfaction rate because 65% is greater than 58%.
• BThe confidence intervals overlap, so there may not be a statistically significant difference between the two companies.
• CThe first company definitely has higher satisfaction because the lower bound of its confidence interval is 60%.
• DThe surveys cannot be compared because they were conducted at different companies.

In a survey of 500 randomly selected employees, 62% reported being satisfied with their workplace, with a margin of error of 4 percentage points. A second survey of 500 randomly selected employees at a different company found that 59% were satisfied, also with a margin of error of 4 percentage points. Based on these surveys, which of the following is true?

• AThe first company definitely has higher employee satisfaction than the second company.
• BThe difference in satisfaction rates is exactly 3 percentage points.
• CThe confidence intervals for the two satisfaction rates overlap.
• DDoubling the sample sizes would make the satisfaction rates equal.

A poll of 2500 randomly selected registered voters found that 41% plan to vote for Candidate X, with a margin of error of 2 percentage points. Based on this poll, which of the following is most likely true?

• ABetween 39% and 43% of the voters in the sample plan to vote for Candidate X.
• BBetween 39% and 43% of all registered voters plan to vote for Candidate X.
• CExactly 41% of all registered voters plan to vote for Candidate X.
• DIf the sample size were reduced to 625, the margin of error would decrease to 1 percentage point.

A university researcher randomly selected 200 faculty members from all faculty members at State University and asked them about their research funding. What is the largest population to which the results of this survey can be generalized?

• AAll faculty members at universities in the state
• BThe 200 faculty members who were surveyed
• CAll faculty members at State University
• DAll university faculty members nationwide

A polling organization surveyed 900 adults and found that 38% approve of a policy proposal, with a margin of error of 3 percentage points. A second poll of 225 adults on the same proposal would most likely have which margin of error?

• A1.5 percentage points
• B3 percentage points
• CBetween 35% and 41%
• D6 percentage points

A survey of 400 randomly selected voters found that 52% support Proposition A, with a margin of error of 5 percentage points. Which of the following best describes what this margin of error means?

• AThe percentage of all voters who support Proposition A is between 47% and 57%.
• BThe percentage of all voters who support Proposition A is between 52% and 57%.
• CIf the survey were repeated with 800 voters, the margin of error would be 10 percentage points.
• DThere is a 5% probability that the survey result is incorrect.