A 2004 Gallup survey interviewed a nationally representative

A 2004 Gallup survey interviewed a nationally representative random sample of 600 teenagers aged 13 to 17; 55 acknowledged having smoked in the past week.

Calculate a 95% confidence interval for the parameter

Solution

CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=55
Sample Size(n)=600
Sample proportion = x/n =0.092
Confidence Interval = [ 0.092 ±Z a/2 ( Sqrt ( 0.092*0.908) /600)]
= [ 0.092 - 1.96* Sqrt(0) , 0.092 + 1.96* Sqrt(0) ]
= [ 0.069,0.115]