Question

itamin 0 , whether ingesteo as a diettry supplement or produced naturally when sunilight fatls upon the swio, is esiential foe strong, healthy panes, The bone diseaif rickets wan largely eliminated during the 1950 s, but now there is concern that a generation of children more likely to wotch TV or plyy computer oames than soend time outdoors is at increautd. nisk. A healtheare provider took a sample of 760 rendomly selected chldren and found 10% of them were deficient in vitamin 0 . (a) In this setting, the condweois for inference ate met because sample sige is iarge - the mumber of wiccesses (np) and the Aurber of fallures (nit-p)lere both iarger than 10 . (i) What it the number of successes? (ii) What is the number of follures? (b) Construet a 94 Wh confidence interval for the true aropoition of children who are deficient in vitamin D (use 4 decimals): 1 (c) How should this interval be incerpreteo? Wo are 94% conedent that the true preportion of chidren deficicot in vaamin D folls within the confidence interval boundi. We are 94w confident that the proportion of viamin D deficiency in a randomly sumpled child fals within the confidence interva bounds. We are 94: confident that the proportion of the sampied 760 children deficient in vitamin 0 talls invide the contidence intervar besund. We are 94. conndent that the proportion of chaden deficient in vitamin D is 10% (d) Evilain what " 94% conhdence": means: 945 of random samples of size 760 will produce that contain the of chisien that are deficient in viamin o (e) Does this study show that computer games are the cause of rickets? Yei, because the bone disease was largety eliminated, and now we are 947 confident that aniy 10% of children have the defciency No, confidence intervais dont address causation. Yea. Since food manufacturers thave increased the amount of vitamin D in their products over the years, it is likely the case thit children plejiog too many camputer games hat caused the increase in rickets. No, the study shons that a change in chidren'y diets over the years is the cave for the increase in rickets.

Answer 1

Vitamin D is essential for healthy bones, and a deficiency can lead to conditions like rickets. A study shows that 10% of randomly selected children were deficient in vitamin D. However, the study does not prove that computer games cause rickets.

Step-by-step explanation:

Vitamin D is essential for healthy bones and is synthesized in the skin when exposed to sunlight. A deficiency in vitamin D can lead to conditions such as rickets in children and osteomalacia in adults. In the given study, a sample of 760 randomly selected children showed that 10% of them were deficient in vitamin D.

To interpret this finding, a 94% confidence interval was constructed, indicating that we can be 94% confident that the true proportion of children deficient in vitamin D falls within the bounds of the interval. However, the study does not establish a causal relationship between computer games and rickets.