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 3400 children randomly selected found 19​% 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.
(_,_)
​(Round to three decimal places as​ needed.)
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 confidence interval bounds.
D.
We are​ 98% confident that the proportion of children deficient in vitamin D is 0.19.

​c) Explain what​ "98% confidence" means.
About​ 98% of random samples of size 3400 will produce ( a true proportion, Sample means, Confidence intervals)
that contain the ( Confidence interval, a true proportion, number) of children that are deficient in vitamin D.

Answer 1

A)

The condition for the confidence interval is satisfied as

b) Explain carefully what the interval means.
option A is right.
We are​ 98% confident that the proportion of children deficient in vitamin D falls inside the confidence interval bounds.

c)

About​ 98% of random samples of size 3400 will produce Confidence intervals
that contain the true proportion of children that are deficient in vitamin D.