Bluebook SAT Test Inference from Sample Statistics and Margin of Error 1

Question 1

A polling organization surveyed a random sample of 400 registered voters in a state and found that 52% support a ballot measure, with a margin of error of ±4 percentage points at a 95% confidence level.
Which of the following is the most appropriate conclusion?

Accepted Answer

Between 48% and 56% of all registered voters in the state likely support the ballot measure.

Answer

Exactly 52% of all registered voters in the state support the ballot measure.

Answer

At least 52% of all registered voters in the state support the ballot measure.

Answer

The ballot measure will pass because more than half the sample supports it.

Question 2

A researcher increases the sample size in a study from 100 to 900 participants. Assuming all other conditions remain constant, what happens to the margin of error?

Accepted Answer

The margin of error is divided by 3.

Answer

The margin of error triples.

Answer

The margin of error is divided by 9.

Answer

The margin of error remains the same.

Question 3

A survey of 600 randomly selected adults found that 43% have a gym membership, with a margin of error of ±3 percentage points. A researcher claims that fewer than 40% of adults have gym memberships. Based on the survey results, which statement best evaluates this claim?

Accepted Answer

The claim is plausible because values below 40% fall just outside the interval, making it uncertain.

Answer

The claim is definitely true because the lower bound of the confidence interval is 40%.

Answer

The claim cannot be ruled out because 40% falls just outside the confidence interval.

Answer

The claim is supported because the sample proportion is above 43%.

Question 4

Two surveys are conducted to estimate the proportion of students who prefer online learning. Survey A samples 200 students and Survey B samples 800 students. Both use random sampling. Which survey will produce a more precise estimate, and why?

Accepted Answer

Survey B, because larger samples produce smaller margins of error.

Answer

Survey A, because smaller samples are easier to control for bias.

Answer

Both surveys are equally precise because both use random sampling.

Answer

Survey A, because larger samples introduce more variability.

Question 5

A 95% confidence interval for the mean daily screen time of teenagers is reported as (5.8 hours, 6.6 hours). Which of the following is a valid interpretation of this interval?

Accepted Answer

If the sampling process were repeated many times, approximately 95% of the resulting intervals would contain the true mean.

Answer

95% of all teenagers have a daily screen time between 5.8 and 6.6 hours.

Answer

There is a 95% probability that the true mean lies between 5.8 and 6.6 hours.

Answer

The sample mean is guaranteed to be 6.2 hours.

Question 6

A nutritionist randomly samples 250 adults and finds their mean daily calorie intake is 2,050 calories with a margin of error of ±120 calories at a 95% confidence level. The recommended intake is 2,000 calories. Which conclusion is best supported?

Accepted Answer

The recommended intake of 2,000 calories is a plausible population mean.

Answer

The population mean is exactly 2,050 calories.

Answer

The recommended intake of 2,000 calories is not a plausible population mean.

Answer

At least 95% of adults consume more than 2,000 calories.

Question 7

A city planner surveys a random sample of 500 residents and finds that 68% support a new park, with a margin of error of ±4.5 percentage points. If the planner uses a larger random sample of 2,000 residents, which of the following best describes the expected change?

Accepted Answer

The margin of error will decrease to approximately ±2.25 percentage points.

Answer

The sample proportion will definitely increase.

Answer

The confidence level will automatically increase to 99%.

Answer

The margin of error will decrease to approximately ±1.5 percentage points.