Question 1192862: 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 99% 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.
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 hat p =0.19 . 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
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! error for conservative 0.5 estimate=z(0.995)*sqrt(0.5*0.5/n)
square both sides
0.0009=6.636*0.25/n
n=6.636*0.25/0.0009=1843.27 or 1944.
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second one 0.03=2.576*.sqrt(0.0969/n)
0.0009=6.635*0.0969/n
n=713.29 or 714.
Really want to make a difference, use less confidence and allow the error to get a little larger...
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