1. A ride-sharing company wants to estimate the mean pickup wait time for trips completed during a certain day. 2....

1. TRANSLATE the problem information

• Given information:
  • Sample size: 144 trips
  • Sample mean wait time: 8.4 minutes
  • Margin of error: 1.2 minutes for 95% confidence interval

• What this tells us: We can construct a 95% confidence interval for the true mean wait time.

2. INFER the confidence interval

• The confidence interval formula is: \(\mathrm{sample\ mean} \pm \mathrm{margin\ of\ error}\)
• Calculation: \(8.4 \pm 1.2 = [7.2, 9.6]\) minutes
• This means we are 95% confident the true population mean lies between 7.2 and 9.6 minutes

3. INFER the correct interpretation

• A confidence interval tells us about the likely range of the population parameter (the true mean)
• It does NOT tell us about individual data points or what percentage of trips fall in this range
• The correct interpretation: "It is plausible that the mean wait time for all trips is between 7.2 and 9.6 minutes"

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about confidence intervals: Students often think confidence intervals describe the distribution of individual data points rather than the range of plausible values for the population parameter.

They reason: "If we're 95% confident, then 95% of the trips must have wait times in this range." This fundamental misunderstanding of what confidence intervals represent leads them to select Choice C (At least 95% of trips had wait times between 7.2 and 9.6 minutes).

Second Most Common Error:

Weak INFER skill: Students treat the sample mean as if it were the exact population mean, not recognizing the uncertainty inherent in sampling.

They think: "The sample mean is 8.4 minutes, so that must be the true mean for all trips." This oversimplification leads them to select Choice A (The mean wait time for all trips is 8.4 minutes).

The Bottom Line:

This problem tests whether students understand that confidence intervals provide ranges of plausible values for population parameters, not descriptions of individual data distributions. The key insight is distinguishing between what we can conclude about the true population mean versus what we can conclude about individual observations.