Question

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 2900 children randomly selected found 21​% 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 correct choice below and fill in any answer boxes within your choice.

A. left parenthesis nothing comma nothing right parenthesis, [. ], [. ]. ​(Round to three decimal places as​ needed.)

B. The conditions of a confidence interval are not satisfied.

b.)Explain carefully what the interval means.

c.) Explain what​ "98% confidence" means.

Answer 1

Sample size, n= 2900

Sample proportion of children deficient in vitamin D , = 0.21

98% confidence interval for the true proportion of children who are deficient in vitamin D

=

=

=

= ( 0.192, 0.228)

b) The confidence interval means that we are 98% confident that the population mean i.e, the mean number of children who have deficiency of vitamin D will liee in the interval ( 0.192, 0.228)

c) Here 98% confidence show our confidence level, as the confidence level increases the interval become wider and hence the vice versa.