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Dr. Jones and Dr. Smith collect data from a random sample of 400 participants. They each create a confidence interval for the same sample data. Dr. Jones decides to construct a 80

1) The width of Dr. Jones' confidence interval will be narrower than the width of Dr. Smith's confidence interval.
2) The width of Dr. Jones' confidence interval will be wider than the width of Dr. Smith's confidence interval.
3) The width of Dr. Jones' confidence interval will be the same as the width of Dr. Smith's confidence interval.
4) Cannot be determined based on the given information.

1 Answer

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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.

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