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Inference from Sample Statistics and Margin of Error Flashcards

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  1. A survey of 400 randomly selected teenagers found that 57% own a smartphone, with a margin of error of ±5 percentage points at 95% confidence. A researcher claims that a majority (more than 50%) of all teenagers own a smartphone. Which statement best evaluates this claim?

    Answer: The claim is supported because the entire confidence interval (52% to 62%) is above 50%.

    The full 95% confidence interval (52% to 62%) lies entirely above 50%, providing strong evidence that a majority owns smartphones.

  2. Which of the following actions will NOT change the margin of error in a survey?

    Answer: Changing the city in which the survey is conducted while keeping the same sample size and confidence level

    Changing the location of the survey does not affect the margin of error, which depends only on sample size, confidence level, and population variability.

  3. A confidence interval for the mean weight of backpacks in a school district is reported as (14.2 lbs, 17.8 lbs) at 95% confidence. A health official claims the true mean backpack weight is 18 lbs. Which conclusion is most appropriate?

    Answer: The official's claim is not supported because 18 lbs is outside the confidence interval.

    Since 18 lbs falls outside the 95% confidence interval (14.2, 17.8), the data do not support the official's claim.

  4. A random sample of 625 college students estimates that the mean hours of sleep per night is 6.8 hours with a margin of error of ±0.4 hours. What sample size would be needed to reduce the margin of error to ±0.2 hours, assuming the same variability?

    Answer: 2,500

    Halving the margin of error requires quadrupling the sample size: 625 × 4 = 2,500.

  5. A polling firm reports that 46% of likely voters support a candidate, with a 95% confidence interval of (41%, 51%). A campaign manager concludes that the candidate is winning because 46% is the sample proportion. Which statement best evaluates this conclusion?

    Answer: The conclusion is not valid because the confidence interval includes values below 50%.

    Because the 95% confidence interval (41%–51%) includes values below 50%, it is plausible that fewer than half of voters support the candidate.

  6. A manufacturer tests a random sample of 100 light bulbs and finds a mean lifespan of 1,200 hours with a margin of error of ±40 hours at 95% confidence. A customer claims the true mean lifespan is at least 1,250 hours. Which assessment is most appropriate?

    Answer: The claim is not supported because 1,250 hours is outside the confidence interval.

    The 95% CI is (1,160, 1,240); since 1,250 lies above this interval, the data do not support the claim of at least 1,250 hours.

  7. A researcher computes a 90% confidence interval and a 99% confidence interval from the same dataset. How do these intervals compare?

    Answer: The 99% confidence interval is wider than the 90% confidence interval.

    A higher confidence level requires a wider interval to capture the true parameter with greater certainty.