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Inference from Sample Statistics and Margin of Error Flashcards

7 cards from real Bluebook SAT Test practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. A researcher surveys a random sample of 625 students and finds that 58% prefer digital textbooks. The margin of error is ±4 percentage points at 95% confidence. The researcher wants to report that a majority (more than 50%) of students prefer digital textbooks. Is this conclusion valid?

    Answer: Yes, because the entire confidence interval (54%–62%) is above 50%.

    The full 95% confidence interval (54%–62%) lies entirely above 50%, providing strong evidence that a majority prefers digital textbooks.

  2. A random sample of 144 packages from a factory has a mean weight of 500 g with a margin of error of ±6 g at 95% confidence. If the sample size is reduced to 36 packages, what is the new margin of error, assuming the same variability?

    Answer: ±12 g

    Reducing the sample size from 144 to 36 divides it by 4, so the margin of error increases by √4 = 2: 6 g × 2 = 12 g.

  3. A 95% confidence interval for the mean number of text messages sent daily by teenagers is (85, 115). A social media analyst claims teenagers send an average of 80 messages per day. Which statement is most accurate?

    Answer: The analyst's claim is not supported because 80 is below the lower bound of the confidence interval.

    Since 80 lies below the entire 95% CI (85–115), the data do not support the analyst's claim of an 80-message average.

  4. A researcher collects a random sample of 400 adults and constructs a 95% confidence interval for the mean commute time: (22 min, 30 min). Which of the following statements about this interval is correct?

    Answer: If the sampling process is repeated many times, approximately 95% of resulting intervals will contain the true mean.

    The correct interpretation of a 95% confidence interval is that the procedure produces intervals that capture the true parameter about 95% of the time across repeated samples.

  5. A researcher surveys 100 randomly selected adults and finds a 95% confidence interval for mean sleep hours of (6.5, 7.5). The researcher doubles the sample size to 200 and recalculates at the same confidence level with the same standard deviation. What happens to the interval width?

    Answer: The interval becomes narrower by a factor of √2.

    Doubling the sample size multiplies the standard error by 1/√2, so the interval width decreases by a factor of √2.

  6. A 95% confidence interval for the proportion of voters who plan to vote early is (0.38, 0.52). An election official claims that the majority (more than 50%) will vote early. Which assessment is most accurate?

    Answer: The claim is not firmly supported because the confidence interval includes values below 0.50.

    Because the confidence interval (0.38–0.52) includes values below 0.50, it is plausible that fewer than half plan to vote early, so the claim of majority is not firmly established.

  7. A study finds that a random sample of 225 high school students has a mean screen time of 4.5 hours per day with a margin of error of ±0.3 hours at 95% confidence. How would the margin of error change if the sample size increased to 900 students, assuming the same standard deviation?

    Answer: It would decrease to ±0.15 hours.

    Quadrupling the sample size from 225 to 900 halves the margin of error: 0.3 ÷ 2 = 0.15 hours.