A recent study of 2500 children randomly selected found 24 o

A recent study of 2500 children randomly selected found 24% of them deficient in vitamin D. Construct the 98% confidence interval for the true proportion of children who are deficient in vitamin D. Explain carefully what the interval means. Explain what \"98% confidence\" means.

Solution

a.) 98% confidence interval is

( p - Z0.01 × (pq/n) , p + Z0.01 × (pq/n))

( 0.24 - 2.327 × ( 0.24 × 0.76/2500) ,0.24 + 2.327 × ( 0.24 × 0.76/2500))

( 0.24 - 2.327 × 0.0085 , 0.24 + 2.327 × 0.0085)

(0.220 , 0.260)

b.) We are 98% confident that the interval containsthe true proportion of children deficient in vitamin D.

c.) About 98%of random sames of size 2500 will produce a confidence intervals that contains the true proportion of children that are deficient in vitamin D.