In spite of the potential safety hazards, some people would like to have an Internet connection in their car.
A preliminary survey of adult Americans has estimated this proportion to be somewhere around 0.30. Use
the given preliminary estimate to determine the sample size required to estimate this proportion with a
margin of error of 0.01. (Round your answer up to the nearest integer.)
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We can use the formula for sample size calculation for estimating a proportion:
n = (z^2 * p * (1-p)) / E^2
Where:
- n is the required sample size
- z is the z-score corresponding to the desired level of confidence (we'll use a 95% confidence level, so z = 1.96)
- p is the estimated proportion (0.30)
- E is the desired margin of error (0.01)
Plugging in the values:
n = (1.96^2 * 0.30 * (1-0.30)) / 0.01^2
n = (3.8416 * 0.30 * 0.70) / 0.0001
n = 0.809 * 21,000
n = 16,989.9
Rounding up to the nearest integer, the required sample size is:
n = 16,990
Therefore, a sample size of 16,990 is required to estimate the proportion with a margin of error of 0.01.
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