stats #6 Vitamin D, whether ingested as a dietary supplement or produced natural

Question

stats #6

Vitamin D, whether ingested as a dietary supplement or produced naturally when sunlight falls upon the skin, is essential for strong, healthy bones. The bone disease rickets was largely eliminated during the 1950s, but now there is concern that a generation of children more likely to watch TV or play computer games than spend time outdoors is at increased risk. A recent study of 3100 children randomly selected found 22% of them deficient in vitamin D. Complete parts a through d a) Construct a 98% confidence interval for the true proportion of children who are deficient in vitamin D. Select the correct choice below and fill in any answer boxes within your choice. D (Round to three decimal places as needed.) @a. B. The conditions of a confidence interval are not satisfied

Explanation / Answer

p = 0.22

n = 3100

Z for 98% confidence interval = Z0.01 = 2.33

Confidence interval = (p + Z0.01 * sqrt(p * (1 - p) / n))

= (0.22 + 2.33 * sqrt(0.22 * 0.78 / 3100))

= (0.22 + 0.017)

= (0.203, 0.237)

Option-A) (0.203, 0.237)

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