Bluebook SAT Test Inference from Sample Statistics and Margin of Error 8

Question 1

A study finds that a 99% confidence interval for the mean is wider than the corresponding 95% confidence interval. A student asks: 'Does the wider interval mean we are less certain about the true mean?' What is the correct response?

Accepted Answer

No, because a wider interval provides more certainty that the true mean is captured.

Answer

A wider confidence interval actually provides greater certainty of capturing the true mean — the trade-off is precision for confidence.

Question 2

A hospital records the blood pressure of 900 randomly selected patients and finds a mean systolic pressure of 118 mmHg with a margin of error of ±2 mmHg at 95% confidence. A health organization defines hypertension risk as a mean above 120 mmHg. Is the organization's threshold consistent with this sample?

Accepted Answer

No, because 120 mmHg is at the upper boundary and values above it fall outside the confidence interval.

Answer

The confidence interval is 116–120 mmHg; 120 is the upper boundary, and values above the threshold fall outside the interval, making the population mean exceeding 120 implausible.

Question 3

A researcher wants to estimate the mean height of adult men in a country to within ±0.5 cm at 95% confidence. The standard deviation is estimated at 7 cm. Using n = (z* × σ / E)² with z* = 2, approximately how large a sample is needed?

Accepted Answer

784 men

Answer

n = (2 × 7 / 0.5)² = (28)² = 784 men.

Question 4

A supermarket surveys a random sample of 900 customers and finds a mean spending of $87 per visit with a standard error of $2. Which statement about the 95% confidence interval is accurate, using z* = 2?

Accepted Answer

The confidence interval is ($83, $91), giving a plausible range for the true mean spending per visit.

Answer

The 95% CI is $87 ± 2($2) = $87 ± $4 = ($83, $91), and it estimates the plausible range for the population mean — not the range of individual customer spending.

Question 5

A confidence interval for mean study hours is (1.8, 3.2). A professor claims students study less than 2 hours on average. Based on the confidence interval, which statement is most accurate?

Accepted Answer

The professor's claim is plausible because values below 2 hours are within the confidence interval.

Answer

Values below 2 hours (down to 1.8) are within the confidence interval, so a true mean below 2 hours is plausible based on the data.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Inference from Sample Statistics and Margin of Error 8