1) Suppose that a health expert has claimed that 21 % of college students smoke
ID: 3154216 • Letter: 1
Question
1) Suppose that a health expert has claimed that 21 % of college students smoke cigarettes. To investigate this claim, researchers survey a random sample of college students. Using this sample, a 98 % confidence interval for the percentage of college students who smoke is found to be 14.08 % to 17.92 %. Based this interval, can we conclude that the claim that 21 % of all college students smoke is reasonable? (Choose one of the following)
A) The claim of 21% is not reasonable because the value 21% is not in the confidence interval.
B)The claim of 21% is reasonable because the value 21% is not in the confidence interval.
C)The claim of 21% is not reasonable because the value 21% is in the confidence interval.
D)The claim of 21% is reasonable because the value 21% is in the confidence interval.
_____________________________
2) Vitamin D is an essential ingredient for maintaining strong bones and teeth. Sources of this vitamin are natural sunlight and certain dietary supplements. There is a growing concern among pediatricians that today's youngsters are spending too much time indoors. This increases the risk of vitamin D deficiency and all of its related health issues. A research team would like to estimate the proportion of children (aged 6 to 12) that currently exhibit a deficiency in this micro-nutrient. The team samples 92 children and find that 46 of them exhibit a deficiency in vitamin D. Their confidence interval for the true proportion of children that exhibit a deficiency in vitamin D is 0.39783 to 0.60217. The approximate confidence level for this interval is:
A) 90%
B) 95%
C)98%
D)99%
Explanation / Answer
1) Suppose that a health expert has claimed that 21 % of college students smoke cigarettes. To investigate this claim, researchers survey a random sample of college students. Using this sample, a 98 % confidence interval for the percentage of college students who smoke is found to be 14.08 % to 17.92 %. Based this interval, can we conclude that the claim that 21 % of all college students smoke is reasonable? (Choose one of the following)
A) The claim of 21% is not reasonable because the value 21% is not in the confidence interval.
B)The claim of 21% is reasonable because the value 21% is not in the confidence interval.
C)The claim of 21% is not reasonable because the value 21% is in the confidence interval.
D)The claim of 21% is reasonable because the value 21% is in the confidence interval.
2) Vitamin D is an essential ingredient for maintaining strong bones and teeth. Sources of this vitamin are natural sunlight and certain dietary supplements. There is a growing concern among pediatricians that today's youngsters are spending too much time indoors. This increases the risk of vitamin D deficiency and all of its related health issues. A research team would like to estimate the proportion of children (aged 6 to 12) that currently exhibit a deficiency in this micro-nutrient. The team samples 92 children and find that 46 of them exhibit a deficiency in vitamin D. Their confidence interval for the true proportion of children that exhibit a deficiency in vitamin D is 0.39783 to 0.60217. The approximate confidence level for this interval is:
A) 90%
B) 95%
C)98%
D)99%
Answer: b).95%
p=46/92 =0.5
standard error = sqrt(0.5*0.5/92) =0.0521
from the interval margin of error = (0.60217-0.39783)/2 = 0.10217
z value =margin of error /se =0.10217/0.0521 =1.961036468
=1.96 ( approximate)
For z=1.96, confidence level =95%
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