Question

3. Sample Size for Motor Vehicle Ownership: You have been hired by the Ford Motor Company to do market research, and you must estimate the percentage of households in which a vehicle is owned. How many households must you survey if you want to be 95% confident that your sample percentage has a margin of error of three percentage points? a) Assume that a previous study suggested that vehicles are owned in 86% of households. Use the rounding rule for the sample size. Show your work. b) Assume that there is no available information that can be used to estimate the percentage of households in which a vehicle is owned. Use the rounding rule for the sample size. Show your work.

Answer 1

a) From standard normal tables, we have:
P( -1.96 < Z < 1.96) = 0.95

Therefore the margin of error here is computed as:

MOE= 2* p(1 - p) n

For a prior proportion value of p = 0.86, we have here:

0.86(1 – 0.86) 0.03 = 1.96 * n

$n = 1.96^2*\frac{0.86(1-0.86)}{0.03^2} = 513.92$

Therefore 514 is the required sample size here.

b) As we dont have a prior proportion value here, we use p = 0.5 to get a conservative value of sample size here as:

$n = 1.96^2*\frac{0.5(1-0.5)}{0.03^2} = 1067.11$

Therefore 1068 is the required sample size here.