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andrew-mc [135]
3 years ago
9

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 2020​% of them deficient in vitamin D. Find a 98% confidence interval.
Health
1 answer:
Hatshy [7]3 years ago
3 0

Answer:

The 98% confidence interval for children deficient in vitamin D is (0.18, 0.22).

Explanation:

The (1 - <em>α</em>)% confidence interval for population proportion <em>p</em> is:

CI=\hat p\pm z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}

The information provided is:

n=3400\\\hat p=0.20\\\alpha =0.02

Compute the critical value of <em>z</em> for 98% confidence interval as follows:

z_{\alpha/2}=z_{0.02/2}=z_{0.01}=2.33

*Use a <em>z</em>-table for the value.

Compute the 98% confidence interval for the population proportion as follows:

CI=\hat p\pm z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}

     =0.20\pm 2.33\times \sqrt{\frac{0.20(1-0.20)}{3400}}

     =0.20\pm 0.0161\\=(0.1839,\ 0.2161)\\\approx (0.18,\ 0.22)

Thus, the 98% confidence interval for children deficient in vitamin D is (0.18, 0.22).

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