Use the given degree of confidence and sample data to construct a confidence int

Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
Of 150 adults selected randomly from one town, 30 of them smoke. Construct a 99% confidence interval for the true percentage of all adults in the town that smoke.
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
Of 150 adults selected randomly from one town, 30 of them smoke. Construct a 99% confidence interval for the true percentage of all adults in the town that smoke.
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
Of 150 adults selected randomly from one town, 30 of them smoke. Construct a 99% confidence interval for the true percentage of all adults in the town that smoke.

Explanation / Answer

p=30/150=0.2

for 99% confidence, the z value is 2.576

the N is 150

thus lower limit is p-z*sqrt(p*(1-p)/N)=0.2-2.576*sqrt(0.2*0.8/150)=0.1159

the upper limit is p+z*sqrt(p*(1-p)/N)=0.22.576*sqrt(0.2*0.8/150)=0.2841

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