Inference from Sample Statistics and Margin of Error Flashcards

A survey estimates the proportion of adults who read at least one book per month. Sample A uses 200 randomly selected adults and Sample B uses 800 randomly selected adults, both from the same population. The sample proportion in both is 0.35. How does the width of the 95% confidence interval from Sample B compare to that from Sample A?

Answer: The interval from Sample B is half as wide as that from Sample A.

Quadrupling the sample size (200 to 800) reduces the margin of error by half, making the confidence interval half as wide.

A 95% confidence interval for the mean number of hours college students spend studying weekly is (12 hours, 18 hours). A professor claims the true mean is exactly 15 hours. Which statement best evaluates this claim?

Answer: The claim is consistent with the data because 15 hours falls within the confidence interval.

Because 15 hours falls within the 95% confidence interval (12, 18), it is a plausible value for the true population mean.

A researcher randomly surveys 100 employees at a company and finds that 40% use public transportation, with a margin of error of ±8 percentage points at 95% confidence. To cut the margin of error to ±4 percentage points, the researcher must survey how many employees?

Answer: 400

Halving the margin of error requires quadrupling the sample size: 100 × 4 = 400.

A study finds a 95% confidence interval of (0.55, 0.75) for the proportion of students who prefer group projects. A teacher claims more than 80% prefer group projects. Which conclusion is most appropriate?

Answer: The teacher's claim is not supported because 0.80 is above the entire confidence interval.

Since 0.80 lies above the upper bound of the 95% CI (0.75), the data do not support the teacher's claim.

A study reports a 95% confidence interval of (2.1 kg, 2.9 kg) for the mean daily food intake of a bird species. A biologist claims the mean daily intake is 3.2 kg. Is this claim supported?

Answer: No, because 3.2 kg is above the upper bound of the confidence interval.

Since 3.2 kg lies above the entire 95% CI (2.1, 2.9), the data do not provide support for the biologist's claim.

A random sample of 576 students finds a mean GPA of 3.1 with a margin of error of ±0.05 at 95% confidence. If the researcher uses a 90% confidence level instead, how does the confidence interval change?

Answer: It becomes narrower.

Decreasing the confidence level from 95% to 90% requires a smaller critical value, producing a narrower confidence interval.

A survey of 500 randomly selected households finds that 29% own two or more vehicles, with a 95% confidence interval of (24.9%, 33.1%). A transportation official states that nearly a third (33%) of households own two or more vehicles. Which statement best evaluates this claim?

Answer: The claim is plausible because 33% falls within the confidence interval.

Since 33% falls just within the 95% confidence interval (24.9%–33.1%), it is a plausible value for the true population proportion.