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In a report by CNN Health News, the headlines read "Study: Junk food raises teens' risk of heart disease." The headlines were based on a study of 249 high school students between the ages of 13 and 18. One researcher said, "more than 80% of those tested were eating a diet that could promote heart disease." Ultrasound was used to measure the thickness of the carotid artery, which, the researcher said, "can be an early indicator of atherosclerosis, an abnormal hardening of the artery walls."
-The conservative margin of error for the sample of 249 students is
A) 0.4%.
B) 6.3%.
C) 14.1%.
D) none of the above.

Question

Use the following information for questions:
 In a report by CNN Health News, the headlines read "Study: Junk food raises teens' risk of heart disease." The headlines were based on a study of 249 high school students between the ages of 13 and 18. One researcher said, "more than 80% of those tested were eating a diet that could promote heart disease." Ultrasound was used to measure the thickness of the carotid artery, which, the researcher said, "can be an early indicator of atherosclerosis, an abnormal hardening of the artery walls."
-The conservative margin of error for the sample of 249 students is
A) 0.4%.
B) 6.3%.
C) 14.1%.
D) none of the above.

Quizplus · Accepted Answer

The conservative margin of error for a sample size of 249 can be calculated using the formula for the margin of error at 95% confidence level, which is approximately 1.96 * sqrt((0.5*0.5)/n), where n is the sample size. Plugging in 249 for n gives a margin of error close to 6.3%. This formula uses 0.5 for the proportion, which provides the maximum possible margin of error (hence "conservative"), as 0.5 maximizes the product p(1-p) in the formula.

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