Question

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.

Answer 1

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%