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 healthcare provider took a sample of 285 randomly selected children and found 20% of them were deficient in vitamin D.

(a) In this setting, the conditions for inference are met because sample size is large — the number of successes and the number of failures are both larger than 10.
(i) What is the number of successes?  
(ii) What is the number of failures?  
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(b) Construct a 94% confidence interval for the true proportion of children who are deficient in vitamin D (use 4 decimals):
( ? , ? )
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(c) What should this interval be interpreted? THIS IS A MULTIPLE CHOICE QUESTION!

A)We are 94% confident that the proportion of children deficient in vitamin D is 20%.

B)We are 94% confident that the proportion of the sampled 285 children who deficient in vitamin D falls inside the confidence interval bounds.    

C)We are 94% confident that the proportion of vitamin D deficiency in a randomly sampled child falls within the confidence interval bounds.

D)We are 94% confident that the true proportion of children deficient in vitamin D falls within the confidence interval bounds.

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Explain what "94% confidence" means: THIS IS A MULTIPLE CHOICE QUESTION
94% of random samples of size 285 will produce ( ? ) confidence intervals a true proportion a sample proportion that contain the ( ? ) confidence interval sample proportion true proportion of children that are deficient in vitamin D.

Produce _____

A) confidence intervals

B) A true proportion

C) a sample proportion

Contain the _______

A) confidence interval

B) sample proportion

C) true proportion

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Does this study show that computer games are the cause of rickets? THIS IS A MULTIPLE CHOICE QUESTION

A) No, confidence intervals don't address causation.

B) Yes, because the bone disease was largely eliminated, and now we are 94% confident that only 20% of children have the deficiency.    

C) Yes. Since food manufacturers have increased the amount of vitamin D in their products over the years, it is likely the case that children playing too many computer games has caused the increase in rickets.

D) No, the study shows that a change in children's diets over the years is the cause for the increase in rickets.

A GED tutoring company would like to estimate the current percentage of non-high school graduates.

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(a) How many people should be surveyed in order to estimate the proportion of non-high school graduates within 8% with 90% confidence?  

(b) Suppose the tutoring company wanted to cut the margin of error to 7%. How many people should be sampled now?  

(c) In a certain rural area, the percent of people who have a GED was thought to be 19%. How many people should be sampled in this region to estimate the proportion without a GED within 3%?

Answer 1

NOTE:-

As per HomeworkLib rule i little bit confused about d(ii) bit.So, i can't answer for that if you want please upload it as another question.THANK YOU......