Problem 4 National Institute of Health (NIH) using a random sample of 400 from t

Question

Problem 4

National Institute of Health (NIH) using a random sample of 400 from the population of US teenagers obtained the following confidence interval for the proportion of US teenagers who smoke cigarettes (01671 02329)

a) What is the number of teenagers in the sample of 400 who smoke cigarettes?

b) What is the margin of error and the confidence level of this interval? c) What is the largest possible margin of error of a 98% confidence interval for the population proportion based on a random sample of size = 400?

Explanation / Answer

Ans:

a)point estmate=sample proportion=(0.2329+0.1671)/2=0.2

number of teenagers who smoke=400*0.2=80

b)Margin of error=CI width/2=(0.2329+0.1671)/2=0.0329

0.0329=z*sqrt(0.2*0.8/400)

0.0329=z*0.02

z=1.645,which is z multiplier for 90% CI.

c)z value of 98% CI is 2.33

Margin of error=2.33*sqrt(0.2*0.8/400)=2.33*0.02=0.0466

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