Bluebook SAT Test Inference from Sample Statistics and Margin of Error 13

Question 1

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?

Accepted Answer

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

Answer

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.

Question 2

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?

Accepted Answer

±1 cm

Answer

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.

Question 3

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?

Accepted Answer

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

Answer

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.

Question 4

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?

Accepted Answer

It will be wider than (1.8, 2.4).

Answer

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

Question 5

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?

Accepted Answer

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

Answer

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%.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Inference from Sample Statistics and Margin of Error 13