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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To determine the required sample size, we need to use the formula:
n = (Z^2 * p * (1-p)) / E^2
Where:
n = required sample size
Z = z-score corresponding to the level of confidence (we will use a 95% confidence level, so the z-score is approximately 1.96)
p = estimated proportion (0.30)
E = margin of error (0.01)
Let's plug 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 = 0.8099 / 0.0001
n = 8099
Rounding up to the nearest integer, the required sample size is 8100.
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