In: Statistics and Probability
A random sample of 200 high school students in a particular town showed that 122 smoke on a regular basis. Find the 99% confidence interval estimating the population percentage for smokers at this high school.
Solution :
Given that,
n = 200
x = 122
Point estimate = sample proportion = = x / n = 122/200 = 0.610
1 - = 0-0.610 = 0.390
At 99% confidence level
= 1-0.99% =1-0.99 =0.01
/2
=0.01/ 2= 0.005
Z/2
= Z0.005 = 2.576
Z/2 = 2.576
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 2.576 * ((0.610*(0.390) /200 )
= 0.089
A 99% confidence interval for population proportion p is ,
- E < p < + E
0.610-0.089 < p < 0.610+0.089
0.521 < p < 0.699
( 0.521. 0.699 )