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 0.03 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 0.03 margin of error? Round your answer
*up* to the nearest whole number.

n = answer ______ 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=0.22

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.

n = answer ______ households

Answer #1

Solution :

Given that,

margin of error = E = 0.03

Z_{/2}
= 1.96

(a)

= 0.5

1 - = 0.5

sample size = n = (Z_{
/ 2} / E)^{2} *
* (1 -
)

= (1.96 / 0.03)^{2} * 0.5 * 0.5

= 1067.1

sample size = n = **1068 households**

(b)

= 0.22

1 - = 0.78

sample size = n = (Z_{
/ 2} / E)^{2} *
* (1 -
)

= (1.96 / 0.03)^{2} * 0.22 * 0.78

= 732.5

sample size = n = **733**
**households**

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