A sample of 400 homeowners includes 124 that expect their home to increase in value in the next year. Find the margin of error of a 99% confidence interval for the percentage of all homeowners with this opinion.
Solution :
Given that,
n = 400
x = 124
Point estimate = sample proportion =
= x / n = 124/400=0.31
1 -
= 1-0.31=0.69
At 99% confidence level the z is ,
= 1 - 99% = 1 - 0.99 =
0.01
/ 2 = 0.01 / 2 = 0.005
Z/2
= Z0.005 = 2.576 ( Using z table )
Margin of error = E = Z
/ 2 *
((
* (1 -
)) / n)
= 2.576 (((0.37*0.69)
/ 400)
= 0.065
=6.5%
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