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 98% level of confidence. a) With no prior research, what sample size should you gather in order to obtain a 0.02 margin of error? Do not round until your final answer.

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
ˆ
p
=
0.215
. Using this new information. what sample size should you gather in order to obtain a 0.02 margin of error? Do not round until your final answer.

n =
households