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 0.025 margin of error at a 99% level of confidence.

a) With no prior research, what sample size should you gather in order to obtain a 0.025 margin of error? Round your answerup 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 ofp=0.21p^=0.21. Using this new information.what sample size should you gather in order to obtain a 0.025 margin of error? Round your answerup to the nearest whole number.

n = households

A research group needs to determine a 90% confidence interval for the mean repair cost for all car insurance small claims. From past research, it is known that the standard deviation of such claims amounts to $90.44.

• If the group wants their estimate to have a maximum error of $16, how many small claims should they sample? Round your answer up to the next integer.