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 3400 children randomly selected found 19% of them deficient in vitamin D. Complete parts a through c below
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 3400 children randomly selected found 19% of them deficient in vitamin D. Complete parts a through c below.
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
?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 people deficient in vitamin D falls inside the confidence interval bounds.
C. We are? 98% confident that the proportion of vitamin D deficiency in a randomly sampled child falls within the confidence interval bounds.
D. We are? 98% confident that the proportion of children deficient in vitamin D is 0.20.2.
?c) Explain what? "98% confidence" means. About? 98% of random samples of size 29002900 will produce ? confidence intervals sample means a true proportion that contain the ? confidence interval number true proportion of children that are deficient in vitamin D.
?d) Does the study show that computer games are a likely cause of? rickets?
A. ?Yes, because the bone disease was largely? eliminated, and now we are? 98% confident that 2020?% of children have the deficiency.
B. ?No, because the interval says nothing about causation.
C. Yes. Since food manufacturers have increased the amount of vitamin D in their products over the? years, it is likely the case that children playing too many computer games has caused the increase in rickets.
D. ?No, because the study suggests that it is more likely the case that a change in? children's diets over the years is the cause for the increase in rickets.
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