The problem involves calculating the confidence interval and interpreting the results based on the information provided:

1. Confidence Interval: The confidence interval for the population mean is already calculated as $(27.1, 33.9)$, and the margin of error is $\pm 3.4$.

2. Interpreting the Results: The correct interpretation depends on understanding the concept of confidence intervals.

   • Correct Answer: A. With 95% confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.

Explanation:

• Confidence Interval: This interval suggests that if you were to take many random samples and calculate the confidence intervals, approximately 95% of them would contain the true population mean.
• Population Mean: This refers to the average commute time of the entire population.
• Incorrect Interpretations:
  • Option B refers to individual commute times, which is incorrect as confidence intervals pertain to the population mean, not individual data points.
  • Option C and D incorrectly generalize the concept of confidence intervals to individual commute times or large samples.

Let me know if you would like detailed calculations or further clarifications.

Follow-up Questions:

1. What is the importance of using a t-distribution instead of a z-distribution in this case?
2. How is the margin of error related to the width of the confidence interval?
3. What factors influence the size of the margin of error in a confidence interval calculation?
4. Why is it important to assume the population is normally distributed for this analysis?
5. How would the confidence interval change if the sample size were larger?

Tip:

When interpreting confidence intervals, always distinguish between conclusions about population means and conclusions about individual data points.