Question

You have been asked to survey a sample of all of the residents within an two-mile radius of the dealership. The area is fairly rural. According to U.S. Census figures, there are only 3,000 residents within a two-mile radius of the dealership. Based upon your knowledge of marketing research, you intend to use a 5% confidence interval. While all residents could identify many different reasons for selecting a car brand, you have concluded that it is binary – and intend to only give them two choices (50%). Keeping with industry standards, you proposed to use a Z-value of 1.96. Given all of the above information, how many residents should you survey? Please show your work in the space provided below.

Answer 1

given data,
survey a sample of all of the residents within an two-mile radius of the dealership.
According to U.S. Census figures, there are only 3,000 residents within a two-mile radius of the dealership.
Assume that,
margin of error is 2%of radius of the dealership
sample proportion is 50%
confidence interval is 95%

Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.05 is = 1.96
Sample Proportion = 0.5
ME = 0.02
n = ( 1.96 / 0.02 )^2 * 0.5*0.5
= 2401 ~ 2401          
residents of survey is 2401