Inference from Sample Statistics and Margin of Error Flashcards

A random sample of 400 registered voters found that 53% plan to vote in an upcoming election, with a margin of error of ±5 percentage points. A news report states 'More than half of registered voters will vote.' Which assessment is most appropriate?

Answer: The statement is not supported because the margin of error is larger than the difference from 50%.

Because 48% (lower bound) is below 50%, the confidence interval does not rule out the possibility that fewer than half plan to vote, so the statement is not firmly supported.

A researcher surveys 81 randomly selected plants and finds a mean height of 42 cm with a margin of error of ±3 cm at 95% confidence. If the sample size is increased to 729 plants (same population), what is the new margin of error?

Answer: ±1 cm

Increasing sample size from 81 to 729 multiplies it by 9, so the margin of error decreases by a factor of √9 = 3: 3 cm ÷ 3 = 1 cm.

A 95% confidence interval for the mean daily steps taken by adults is (7,200, 8,800). A fitness app company claims the true mean is 9,000 steps. Which conclusion is best?

Answer: The claim is not supported; 9,000 is outside the confidence interval.

Since 9,000 steps lies above the upper bound of the 95% confidence interval (8,800), the data do not support the company's claim.

A national health survey asks 600 randomly selected adults about their fruit consumption. The 95% confidence interval for the mean servings per day is (1.8, 2.4). Researchers want to report a 99% confidence interval from the same data. How will the new interval compare?

Answer: It will be wider than (1.8, 2.4).

Increasing the confidence level from 95% to 99% requires a larger critical value, producing a wider confidence interval from the same data.

Two surveys estimate the proportion of adults who prefer tea over coffee. Survey X uses a random sample of 400 people and reports a margin of error of ±5%. Survey Y uses a random sample of 1,600 people and reports a margin of error of ±2.5%. Which survey allows for a more precise estimate of the population proportion?

Answer: Survey Y, because the larger sample size produces a smaller margin of error.

A smaller margin of error means a more precise estimate; Survey Y's ±2.5% margin of error makes it more precise than Survey X's ±5%.

A medical study uses a random sample of 500 patients to estimate the mean reduction in blood pressure after taking a new drug. The 95% confidence interval is (8 mmHg, 14 mmHg). A doctor claims the drug reduces blood pressure by at least 15 mmHg on average. Which statement is most accurate?

Answer: The doctor's claim is not supported because 15 is above the entire confidence interval.

Since 15 mmHg lies above the upper bound of the 95% CI (14 mmHg), the data do not support the doctor's claim of at least a 15 mmHg reduction.

A pollster surveys a random sample of 1,000 adults and reports that 42% support a tax increase, with a margin of error of ±3 percentage points at 95% confidence. Which of the following conclusions is most justified?

Answer: We can be 95% confident that the true proportion of adults who support the tax increase is between 39% and 45%.

The 95% confidence interval (39%–45%) represents the range of plausible values for the true population proportion at the stated confidence level.