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 0.035 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 0.035 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 $\displaystyle \hat{{{p}}}={0.21}$ . Using this new information. what sample size should you gather in order to obtain a 0.035 margin of error? Round your answer up to the nearest whole number.

n = households