Answered: In a sample of 100 children, 6 were…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.3: Conditional Probability; Independent Events; Bayes' Theorem

Problem 82E

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In a sample of 100 children, 6 were found to be Vitamin D deficient. In your work below, use the Wilson-adjusted sample proportion p̃ rather than p̂.

(a) Find a 99% CI for the proportion of all children who are Vitamin D deficient.

(b) Find a 95% CI for the proportion of all children who are Vitamin D deficient.

(c) If the sample were 12 of 200 (rather than 6 of 100) Vitamin D deficient, compared to
the CI you found in (b), the CI would now be (circle one):
Narrower Wider Same

d) Suppose that we want to find a 95% CI whose total width is .02, that is, we want tα/2⋅ SEP̃ ≤ .01. What sample size n would we need? In finding n, let’s assume that we do not know what the sample proportion p̃ will be.

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