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 0.02 margin of error at a 80% level of confidence.

a) With no prior research, what sample size should you gather in order to obtain a 0.02 margin of error? Round your answer up to the nearest whole number.

n = 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=0.235

. Using this new information. what sample size should you gather in order to obtain a 0.02 margin of error? Round your answer up to the nearest whole number.

n = households

Answer 1

Solution :

Given that,

margin of error = E = 0.02

Z_/2 = 1.28

(a)

= 0.5

1 - = 0.5

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

= (1.28 / 0.02)² * 0.5 * 0.5

= 1024

sample size = n = 1024

(b)

= 0.235

1 - = 0.765

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

= (1.28 / 0.02)² * 0.235 * 0.765

= 737

sample size = n = 737