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

Yes, because a wider interval captures less information.

Answer

Yes, because the sample size must have been smaller for the 99% interval.

Answer

No, because both intervals have the same margin of error.

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

Yes, because 120 mmHg is within the confidence interval of 116–120 mmHg.

Answer

Yes, because the sample mean of 118 is close enough to 120 to be equivalent.

Answer

No, because confidence intervals cannot be used to evaluate health thresholds.

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

196 men

Answer

49 men

Answer

2,401 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 confidence interval is ($85, $89), meaning 95% of customers spend in this range.

Answer

The confidence interval is ($83, $91), and 95% of individual customers spend in this range.

Answer

The confidence interval is ($85, $89), and the true mean is guaranteed to be $87.

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

The professor's claim is definitely false because the midpoint is 2.5 hours.

Answer

The professor's claim is not plausible because 2 hours is above the lower bound of the interval.

Answer

The professor's claim is true because 1.8 is in the interval.

Question 6

A random sample of 50 employees has a mean commute time of 35 minutes. The margin of error at 95% confidence is ±6 minutes. If the sample size increases to 200, what is the new margin of error?

Accepted Answer

±3 minutes

Answer

±12 minutes

Answer

±1.5 minutes

Answer

±24 minutes

Question 7

A random sample of 100 trees in a forest finds a mean height of 42 feet with a 95% confidence interval of (39, 45). A forest manager claims the true mean is 46 feet. Which evaluation is correct?

Accepted Answer

The claim of 46 feet is not plausible because it falls above the upper bound of the confidence interval.

Answer

The claim of 46 feet is plausible because it is close to the upper bound.

Answer

The claim is plausible because the sample size of 100 is too small to rule out 46 feet.

Answer

The claim is plausible because the margin of error makes all values near 45 possible.