Final answer:
The width of Dr. Jones' 80% confidence interval will be narrower than the width of Dr. Smith's 95% confidence interval because a lower confidence level requires a smaller area under the normal distribution curve.
Step-by-step explanation:
Dr. Jones and Dr. Smith collect data from a random sample of 400 participants to construct confidence intervals. If Dr. Jones chooses to construct an 80% confidence interval while Dr. Smith opts for a 95% confidence interval, we must consider how confidence levels impact the width of the interval. The given reference information illustrates that as the confidence level increases—from 90% to 95%, and up to 99%—the width of the confidence interval also increases. This is due to the necessity to cover a larger area under the normal distribution curve to ensure the interval contains the true population mean with higher certainty. Based on this understanding, the answer to the student's question is: 1) The width of Dr. Jones' confidence interval will be narrower than the width of Dr. Smith's confidence interval. This is because Dr. Jones is constructing an 80% confidence interval, which requires a smaller area under the curve compared to Dr. Smith's 95% interval, resulting in a narrower interval.