In: Statistics and Probability
In a random sample of 125 students, you find that 15 have tattoos (that’s 12%). Construct a 95% confidence interval for the true population proportion of students that have tattoos.
Solution :
Given that,
n = 125
x = 15
Point estimate = sample proportion =
= x / n =0.12 given
1 -
= 1-0.12 =0.88
At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z/2
= Z0.025 = 1.96 ( Using z table )
Margin of error = E = Z/2 *
(((
* (1 -
)) / n)
= 1.96 (((0.12*0.88)
/125 )
E = 0.057
A 95% confidence interval for population proportion p is ,
- E < p <
+ E
0.12-0.057 < p < 0.12+0.057
0.063<p<0.177