2 (7,12,13)-Ogbonna Hopkins Page 1 Vitamin D, whether ingested as a dietary supp

Question

2 (7,12,13)-Ogbonna Hopkins Page 1 Vitamin D, whether ingested as a dietary supplement or produced naturally when sunlight falls upon the skin, is essent for strong. healthy bones. The bone disease rickets was largely eliminated during the 1950s, but now there is concem 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 2400 children randomly selected found 22% of them deficient in vitamin D. Complete parts a through c below. a) Construct a 98% confidence interval for the true proportion of children who are deficient in vitamin D. Select the choice below and fill in any answer boxes within your choice. correct O A. Round to three decimal places as needed.) O B. The conditions of a confidence interval are not satisfied b) Explain carefully what the interval means A. We are 98% confident that the proportion of children deficient in vitamin D falls inside the confidence interval bounds. B. We are 98% confident that the proportion of vitamin D deficiency in a randomly sampled child falls within the confidence interval bounds C. We are 98% confident that the proportion of people deficient in vitamin D falls inside the ? D. We are 98% confident that the proportion of children deficient in vitamin D is 0.22. c) Explain what "98% confidence" means. About 98% of random samples of size 2400 will produce (1) confidence interval bounds. that contain the (2)of children that are deficient in vitamin D (1) O confidence intervals (2) O confidence interval O sample means C a true proportion C true proportion O number

Explanation / Answer

Solution:- Given that n = 2400, p = 22% = 0.22, q = 0.78

a) 98% confidence interval for the true proportion of children = p +/- Z*sqrt(pq/n)
= 0.22 +/- 2.33*sqrt(0.22*0.78/2400)
= 0.200 , 0.240

b) option A.

c)option (2)

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