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

Exactly 74 points

Answer

Between 74 and 79 points

Answer

Less than 74 points

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

Yes, because $130 is close to the lower bound of the interval.

Answer

Yes, because the sample mean is greater than $130.

Answer

No, because the sample mean equals the true 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

Candidate A is definitely winning because both samples show more than 50% support.

Answer

The two surveys contradict each other because their point estimates differ.

Answer

Candidate A's true support is exactly 56%.

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

19% to 22%

Answer

22% to 25%

Answer

16% to 28%

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 the confidence level from 90% to 99%

Answer

Decreasing the sample size from 500 to 200

Answer

Using a convenience sample instead of a random sample

Question 6

A 95% confidence interval for the proportion of customers satisfied with a product is (0.62, 0.78). What is the sample proportion and the margin of error?

Accepted Answer

Sample proportion = 0.70, margin of error = 0.08

Answer

Sample proportion = 0.62, margin of error = 0.16

Answer

Sample proportion = 0.78, margin of error = 0.08

Answer

Sample proportion = 0.70, margin of error = 0.16

Question 7

A 95% confidence interval for the mean commute time in a city is (28 min, 36 min). A city official claims the mean commute time is over 38 minutes. Which statement is most accurate?

Accepted Answer

The claim is not supported because 38 falls outside the confidence interval.

Answer

The claim is supported because 38 is near the upper bound.

Answer

The claim is supported because the sample mean is 32 minutes.

Answer

The claim cannot be evaluated without knowing the exact sample size.