In: Statistics and Probability
Suppose a survey of 500 people age 18 to 34 indicated that 32.2% of them live
with one or both of their parents. Calculate and interpret a confidence interval estimate for the true proportion
of all people age 18 to 34 who live with one or both parents. Use a 94% confidence level.
Solution :
Given that,
n = 500
Point estimate = sample proportion =
= 0.322
1 -
= 1-0.322=0.678
At 94% confidence level
= 1 - 94%
= 1 - 0.94 =0.06
/2
= 0.03
Z/2
= Z0.03 = 1.881 ( Using z table )
Margin of error = E = Z
/ 2 *
((
* (1 -
)) / n)
=1.881 (((0.322*0.678)
/500 )
E = 0.0393
A 94% confidence interval for population proportion p is ,
- E < p <
+ E
0.322 -0.0393< p < 0.322 +0.0393
0.2827< p < 0.3613
The 94% confidence interval for the population proportion p is : 0.2827< p < 0.3613