Bluebook SAT Test Inference from Sample Statistics and Margin of Error 6

Question 1

A news organization reports a poll result: 'The approval rating for the mayor is 61%, with a margin of error of ±4 percentage points.' Which of the following is not a valid conclusion?

Accepted Answer

The approval rating is exactly 61% for the entire population.

Answer

The true approval rating is likely between 57% and 65%.

Answer

A true approval rating of 64% is consistent with the poll results.

Answer

The poll results are consistent with a true approval rating below 65%.

Question 2

A pharmaceutical company tests a new drug on a random sample of 900 patients and finds that 73% showed improvement. The margin of error is ±3%. A regulator requires at least 70% improvement rate in the population for approval. Based on the confidence interval, should the drug be approved?

Accepted Answer

Yes, because the entire confidence interval (70%–76%) is at or above 70%.

Answer

No, because 73% is too close to 70% to be certain.

Answer

No, because the margin of error makes the true proportion uncertain.

Answer

Yes, because the sample proportion is always the true proportion.

Question 3

In a confidence interval (p̂ − E, p̂ + E), what does E represent?

Accepted Answer

The margin of error

Answer

The exact population proportion

Answer

The standard deviation of the population

Answer

The sample size needed for precision

Question 4

A psychologist samples 169 volunteers and records a mean reaction time of 285 milliseconds with a standard error of 6 ms. Using a critical value of 2, what is the 95% confidence interval?

Accepted Answer

(273, 297)

Answer

(279, 291)

Answer

(283, 287)

Answer

(269, 301)

Question 5

A university estimates from a random sample that 80% of its students are satisfied with campus dining, with a margin of error of ±6%. The administration claims that fewer than 75% of students are actually satisfied. Does the data support this claim?

Accepted Answer

No, because 75% is below the lower bound of the confidence interval.

Answer

Yes, because the lower bound is 74%, which is below 75%.

Answer

No, because the entire confidence interval (74%–86%) includes values well above 75%.

Answer

Yes, because 80% minus the margin of error is near 75%.

Question 6

A survey asks 1,000 randomly selected adults whether they support a policy, and 58% say yes with a margin of error of ±3%. A separate survey of 250 randomly selected adults finds 56% say yes with a margin of error of ±6%. Are the two surveys consistent?

Accepted Answer

Yes, because the confidence intervals (55%–61% and 50%–62%) overlap.

Answer

No, because the point estimates differ by 2 percentage points.

Answer

No, because surveys of different sizes cannot be compared.

Answer

Yes, but only if both were conducted by the same organization.

Question 7

A researcher claims that margin of error only depends on sample size. A statistician disagrees. Which factor, besides sample size, also affects margin of error?

Accepted Answer

The confidence level chosen

Answer

The mean of the population

Answer

Whether the sample is from a rural or urban area

Answer

The number of researchers analyzing the data