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 sample size required to estimate the proportion with a margin of error of 0.01, we can use the formula:
n = (z^2 * p * (1-p)) / (E^2)
Where:
n = sample size
z = z-score corresponding to the desired level of confidence (typically 1.96 for a 95% confidence level)
p = estimated proportion of the population (0.30)
E = 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 = 0.8064 / 0.0001
n = 8064
Thus, the sample size required to estimate the proportion with a margin of error of 0.01 is 8064.
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