In: Statistics and Probability
We wish to estimate what percent of adult residents in a certain
county are parents. Out of 500 adult residents sampled, 215 had
kids. Based on this, construct a 95% confidence interval for the
proportion pp of adult residents who are parents in this
county.
Give your answers as decimals, to three places.
< pp <
Solution :
Given that,
n = 500
x = 215
Point estimate = sample proportion = = x / n = 215/500=
1 - = 1-0.43=0.57
At 95% confidence level
= 1 - 95%
= 1 - 0.95 =0.05
/2
= 0.025
Z/2
= Z0.025 = 1.96 ( Using z table )
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 1.96 (((0.43*0.57) /500 )
= 0.043
A 95% confidence interval for population proportion p is ,
- E < p < + E
0.43-0.043 < p <0.43+ 0.043
0.387< p < 0.473
The 95% confidence interval for the population proportion p is : 0.387, 0.473