Bluebook SAT Test Inference from Sample Statistics and Margin of Error 2

Question 1

A school district reports that a random sample of 350 students had a mean math score of 74 with a margin of error of ±5 points. Which of the following best describes the plausible range for the true mean score of all students in the district?

Accepted Answer

Between 69 and 79 points

Answer

The margin of error of ±5 is subtracted and added to the sample mean of 74, giving a plausible range of 69 to 79.

Question 2

A sample of 100 households shows an average electricity bill of $145 per month with a margin of error of ±$12. A researcher claims the true average is less than $130. Is this claim consistent with the survey results?

Accepted Answer

No, because $130 is below the confidence interval of $133–$157.

Answer

The confidence interval runs from $133 to $157; since $130 falls below the lower bound, it is not a plausible value for the population mean.

Question 3

A random sample of 1,600 voters shows 55% prefer Candidate A, with a margin of error of ±2.5%. Another survey of 400 voters shows 57% prefer Candidate A, with a margin of error of ±5%. Which statement is best supported?

Accepted Answer

The larger sample's estimate is more reliable because it has a narrower margin of error.

Answer

A larger sample produces a narrower margin of error, making the estimate from 1,600 voters (±2.5%) more precise and reliable than the estimate from 400 voters (±5%).

Question 4

A health survey of 900 adults estimates that 22% are classified as having high blood pressure, with a margin of error of ±3 percentage points at 95% confidence. What is the range of values consistent with the survey at this confidence level?

Accepted Answer

19% to 25%

Answer

The confidence interval is 22% ± 3%, giving a range from 19% to 25%.

Question 5

Which change to a study design would most directly decrease the margin of error in estimating a population proportion?

Accepted Answer

Increasing the sample size from 200 to 800

Answer

Increasing sample size directly decreases the margin of error; the other options either increase it, maintain it, or introduce bias without improving precision.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Inference from Sample Statistics and Margin of Error 2