Inference from Sample Statistics and Margin of Error Flashcards
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A polling organization surveyed a random sample of 400 registered voters in a state and found that 52% support a ballot measure, with a margin of error of ±4 percentage points at a 95% confidence level. Which of the following is the most appropriate conclusion?
Answer: Between 48% and 56% of all registered voters in the state likely support the ballot measure.
The margin of error creates a confidence interval of 52% ± 4%, meaning the true population proportion is plausibly between 48% and 56%.
A researcher increases the sample size in a study from 100 to 900 participants. Assuming all other conditions remain constant, what happens to the margin of error?
Answer: The margin of error is divided by 3.
Margin of error is proportional to 1/√n; increasing n from 100 to 900 means √900/√100 = 3, so the margin of error is divided by 3.
A survey of 600 randomly selected adults found that 43% have a gym membership, with a margin of error of ±3 percentage points. A researcher claims that fewer than 40% of adults have gym memberships. Based on the survey results, which statement best evaluates this claim?
Answer: The claim is plausible because values below 40% fall just outside the interval, making it uncertain.
The 95% confidence interval is 40%–46%; since 40% is the lower bound, values below 40% are just outside the plausible range, making the claim unlikely but the result is close enough to warrant caution.
Two surveys are conducted to estimate the proportion of students who prefer online learning. Survey A samples 200 students and Survey B samples 800 students. Both use random sampling. Which survey will produce a more precise estimate, and why?
Answer: Survey B, because larger samples produce smaller margins of error.
A larger sample size reduces the margin of error (proportional to 1/√n), producing a more precise estimate of the population proportion.
A 95% confidence interval for the mean daily screen time of teenagers is reported as (5.8 hours, 6.6 hours). Which of the following is a valid interpretation of this interval?
Answer: If the sampling process were repeated many times, approximately 95% of the resulting intervals would contain the true mean.
A confidence interval means that under repeated sampling, 95% of such intervals would capture the true population mean — it does not assign probability to a fixed parameter.
A nutritionist randomly samples 250 adults and finds their mean daily calorie intake is 2,050 calories with a margin of error of ±120 calories at a 95% confidence level. The recommended intake is 2,000 calories. Which conclusion is best supported?
Answer: The recommended intake of 2,000 calories is a plausible population mean.
The confidence interval is 1,930–2,170 calories; since 2,000 falls within this range, it is a plausible value for the true population mean.
A city planner surveys a random sample of 500 residents and finds that 68% support a new park, with a margin of error of ±4.5 percentage points. If the planner uses a larger random sample of 2,000 residents, which of the following best describes the expected change?
Answer: The margin of error will decrease to approximately ±2.25 percentage points.
Quadrupling the sample size (500 to 2,000) reduces the margin of error by a factor of √4 = 2, from ±4.5% to approximately ±2.25%.