Question

You work for a marketing firm that has a large client in the automobile industry. You have been asked to estimate the proportion of households in Chicago that have two or more vehicles. You have been assigned to gather a random sample that could be used to estimate this proportion to within a 0.03 margin of error at a 95% level of confidence.

a) With no prior research, what sample size should you gather in order to obtain a 0.03 margin of error? Round your answer up to the nearest whole number.

n = answer ______ households

b) Your firm has decided that your plan is too expensive, and they wish to reduce the sample size required. You conduct a small preliminary sample, and you obtain a sample proportion of ˆp=0.22

Using this new information. what sample size should you gather in order to obtain a 0.03 margin of error? Round your answer up to the nearest whole number.

n = answer ______ households

Answer 1

Solution :

Given that,

margin of error = E = 0.03

Z_/2 = 1.96

(a)

= 0.5

1 - = 0.5

sample size = n = (Z _{/ 2} / E)² * * (1 - )

= (1.96 / 0.03)² * 0.5 * 0.5

= 1067.1

sample size = n = 1068 households

(b)

= 0.22

1 - = 0.78

sample size = n = (Z _{/ 2} / E)² * * (1 - )

= (1.96 / 0.03)² * 0.22 * 0.78

= 732.5

sample size = n = 733 households