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 0.40. Use the given preliminary estimate to determine the sample size required to estimate this proportion with a margin of error of 0.02. (Round your answer up to the nearest integer.)
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To determine the sample size required, 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 (we'll use 1.96 for 95% confidence)
P = estimated proportion (0.40)
E = margin of error (0.02)
n = (1.96^2 * 0.40 * (1-0.40)) / 0.02^2
n = 3.8416 * 0.40 * 0.60 / 0.0004
n = 0.922464 / 0.0004
n = 2316.16
Rounding up to the nearest integer, the sample size required is 2317.
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