Inference from Sample Statistics and Margin of Error Flashcards

A quality-control team randomly selects 196 bottles from a production line and measures their fill volume. The mean fill is 500 mL with a margin of error of ±2 mL at 95% confidence. If the team wants the margin of error to be ±1 mL with the same confidence level, how many bottles should be sampled?

Answer: 784

Halving the margin of error requires quadrupling the sample size: 196 × 4 = 784.

A 95% confidence interval for the proportion of adults who floss daily is (0.22, 0.34). A dentist claims that fewer than 20% of adults floss daily. Which statement best evaluates this claim?

Answer: The claim is not supported because 0.20 is below the entire confidence interval.

The entire 95% confidence interval (0.22–0.34) lies above 0.20, providing evidence against the dentist's claim that fewer than 20% floss daily.

Two random samples are taken from the same population: Sample 1 has n = 100 and Sample 2 has n = 400. Both samples estimate the same proportion. The 95% margin of error for Sample 1 is approximately 10%. What is the approximate margin of error for Sample 2?

Answer: 5%

Quadrupling the sample size halves the margin of error: 10% ÷ 2 = 5%.

A national survey of 1,200 randomly selected adults finds that 48% prefer reading physical books over e-books, with a margin of error of ±2.8 percentage points at 95% confidence. An author claims that a majority of adults prefer physical books. Which evaluation is most appropriate?

Answer: The claim is not supported because the entire confidence interval (45.2%–50.8%) includes values below 50%.

The confidence interval includes values both below and above 50%, so a majority preference for physical books is possible but not established.

A researcher increases the confidence level of a study from 95% to 99% while keeping all other aspects the same. What effect does this have on the confidence interval?

Answer: The interval becomes wider.

Increasing the confidence level requires a larger critical value, which widens the confidence interval.

A survey finds that 65% of students at a high school support later school start times, with a margin of error of ±4 percentage points at 95% confidence. Which of the following is NOT a valid conclusion from this result?

Answer: Exactly 65% of all students at the school support later start times.

A confidence interval estimates a range for the population proportion; it cannot establish that the true proportion is exactly equal to the sample proportion.

A researcher claims that women in a city sleep an average of 7.5 hours per night. A random sample of 225 women yields a mean of 7.2 hours with a margin of error of ±0.4 hours at 95% confidence. Is the researcher's claim consistent with the data?

Answer: Yes, because 7.5 hours falls within the 95% confidence interval of (6.8, 7.6).

The 95% CI is 7.2 ± 0.4 = (6.8, 7.6); since 7.5 falls within this interval, the researcher's claim is consistent with the data.